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| WBBSE class 10 physical science current electricity notes. |
''Today we will discuss WBBSE class 10 physical science 6th chapter Current Electricity. I hope all the secondary students will be very useful.``
Q. Write down Coulomb's law.
⇒ Coulomb's law: The force (attractive or repulsive) between two point charges at rest is directly proportional to the product of the magnitude of the charges and inversely proportional to the square of the distance between them.
Let two point charges `q_1` and `q_2` are separated by a distance `r`. Now if F is the force between them, then according to Coulomb's law,
`F` ∝ `q_1q_2` [when r is constant] and
`F` ∝ `frac{1}{r^2}` [when`q_1`,`q_2` are constant]
Combining the above two conditions, we get
`F` ∝ `frac{q_1q_2}{r^2}`
`F` = `K frac{q_1q_2}{r^2}`
where k is a proportionality constant called coulomb constant.
Q. The value of Coulomb constant depends on which factors?
⇒ The value Coulomb constant depends on (1) the surrounding medium and (2) the system of units used.
Q. Coulomb's law is applicable in which cases?
⇒ Coulomb's law applies only to (1) point charges and (2) static electric charges.
Q. What are the units of charge in CGS system and SI? Define them. What is the relation between them?
⇒ Units of charge in CGS system and in Sl are respectively esu of charge or statcoulomb and Coulomb.
⬜ 1 esu charge: If two point charges of the same magnitude and of the same nature are placed in vacuum 1 cm apart and exert a repulsive force of 1 dyn on each other, then each charge is called 1 esu of charge or 1 statcoulomb.
1 coulomb charge: If two point charges of the same amount and of the same nature are placed in vacuum at a distance of 1 m and exert a repulsive force of 9 x `10^9` N on each other, then each charge is called 1 C (coulomb).
⬜ 1 C = 3 x `10^9` esu of charge.
Q. Define electric potential. What are the units of electric potential in CGS system and SI? Define them.
⇒ Electric potential: Work done in bringing a unit positive charge from infinity to any point in an electric field is called the electric potential at that point.
If W is the work done in bringing a charge +Q from infinity to a point in the electric field, then the potential at that point is, `V = frac{W}{Q}`
⬜ Units of electric potential in CGS system and Sl are esu of potential or statvolt (stat V) and volt (V) respectively.
⬜ 1 esu of potential or statvolt: If 1 erg of work has to be done in bringing a positive charge of 1 esu from infinity to a point in the electric field, then the potential at that point is called 1 esu of potential or 1 statvolt.
1-volt potential: If 1 J of work has to be done in bringing a positive charge of 1 C from infinity to a point in the electric field, then the potential at that point is called 1 volt.
Q. Establish a relationship between esu of potential and volt (V).
⇒ We know that, If W is the work done in bringing a charge +Q from infinity to a point in the electric field, then the potential at that point is, `V = frac{W}{Q}`
ஃ `1 V` = `frac{1 J}{1 C}`= `frac{10^7 erg}{3\times10^9 esu}`
= `frac{1}{300}` esu of potential
ஃ 1 esu of potential or statV = 300 V
Q. What is potential difference? What are the units of electric potential difference in CGS system and SI ? Define them.
⇒ Potential difference: The amount of work done in bringing a unit positive charge from one point to another point in an electric field, is called the potential difference between the points.
If W is the work done in bringing a charge +Q from one point to another point in the electric field, then the potential difference between these two points is, `V = frac{W}{Q}`
◼ Units of electric potential difference in CGS system and Sl are esu of potential or statvolt (stat V) and volt (V) respectively.
◼ 1 esu of potential difference: If 1 erg of work has to be done in bringing 1 esu of positive charge from one point to another point in an electric field, then the potential difference between these two points is called 1 esu of potential difference.
`1 stat V` = `frac{1 erg}{1 esu}`
1 volt of potential difference: If 1 joule of work has to be done in bringing 1 C of positive charge from one point to another point in an electric field, then the potential difference between these two points is called 1 volt of potential difference.
`1 V` = `frac{1 J}{1 C}`
Q. Is electrical potential a scalar or a vector quantity? What do you mean by potential at a point is 1 volt ? Write the dimension of electric potential.
⇒ Electric potential is a scalar quantity.
◼ The electrical potential at a point is said to be `1` volt if the amount of work done in bringing a `1 C` positive charge from infinity to that point in the electric field is `1 J`.
◼ The dimension of electric potential = `[ML ^ 2T ^ -3I ^ -1]`
Q. What is electric current?
⇒ Electric current: The amount of electric charge flowing per second through any cross-section of a conductor is called the amount of electric current in that conductor.
If `Q` amount of charge flows through any cross section of a conductor in `t` seconds, then the amount of electric current in that conductor is `I = frac{Q}{t}`.
Q. Is electric current a scalar or a vector quantity? What are the CGS and SI units of electric current? What do you mean by 1 ampere?
⇒ Electric current is a scalar quantity.
◼ The CGS unit of electric current is emu and SI and the practical unit is ampere (A).
◼ 1 ampere: If `1 C` electric current flows through any cross-section of a conductor in 1 second, then the amount of electric current through that conductor is said to be 1 ampere (`A`).
`1 A` =` frac {1 C} {1 s}`
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| WBBSE class 10 physical science Current electricity notes. |
Q. Write down Ohm's law.
⇒ Ohm's law: When temperature and other physical conditions of a conductor remain constant, the amount of current flowing through a conductor is directly proportional to the potential difference between the two ends of the conductor.
If the current flowing through a conductor is I when the potential difference across its two ends is V, then according to Ohm's law,
`I` ∝ `V`
or, `I = K V` [ where K is the proportionality constant]
or, `V = frac{1}{K}\times I`
or, `V = RI` [where `frac{1}{K}`= `R` (constant)]
The constant `R` is called the resistance of the conductor.
Q. What do you mean by resistance of a conductor ? What is the unit of resistance in SI? What is its dimension?
⇒ Resistance: Resistance is the property of a conductor due to which it obstructs the flow of current through it.
Or,
Resistance: The property of a conductor by virtue of which it obstructs the flow of current through it is called resistance of the conductor.
◼ Unit of resistance in Sl is ohm (Ω).
◼ Dimension of resistance is `[ML^2T^-3I^-2]`
Q. Define resistance from Ohm's law.
⇒ If the current flowing through a conductor is `I` when the potential difference across its two ends is `V`, then according to Ohm's law,
`V = RI` [where R is the resistance of the conductor]
Or, `R = frac{V}{I}`
Thus, the resistance of a conductor is defined as the ratio between the potential difference across the conductor and the amount of current flowing through the conductor.
Q. What is meant by '' Resistance of a conductor is 1 ohm''? Write the dimension of resistance.
⇒ ''Resistance of a conductor is 1 ohm'' means that `1 A` current will flow through the conductor if` `1 V` potential difference is applied across the conductor.
◼ Dimension of resistance = `[ML^2T^-3I^-2]`
Q. What are ohmic and non-ohmic conductors? Give example.
⇒ Ohmic conductors: The conductors which obey Ohm's law for a wide range of current strength and potential difference are called ohmic conductors.
Example: all metallic conductors.
Non-ohmic conductors: The conductors which do not obey Ohm's law for a wide range of current strength and potential difference are called non-ohmic conductors.
Example: semiconductors, electrolytic solution.
Q. Draw the graph I - V for ohmic conductors.
⇒ In the case of ohmic conductors, the `I - V` graph will be a straight line passing through the origin.
Q. What is the internal resistance of the cell? The internal resistance of the cell depends on which factors?
⇒ The internal resistance of the cell: The resistance offered by the active liquid present inside a cell is called the internal resistance of the cell.
◼ The internal resistance of the cell depends on the following factors ----
(1) Distance between the electrodes: As the distance between the electrodes increases, the internal resistance of a cell increases.
(2) Immersed area of the electrodes: As the Immersed area of the electrodes increases, the internal resistance of the cell decreases.
(3) Nature of the active liquid: As the conductivity of the active fluid increases, the internal resistance of the cell decreases.
(4) Temperature of the active liquid: As the temperature of the active liquid increases, the internal resistance decreases.
Q. Establish the relationship between the EMF and the internal resistance of a cell.
⇒ Suppose a circuit is formed by connecting an electric cell of emf `E`, internal resistance `r`, and an external resistance `R`.
ஃ The equivalent resistance of the circuit = R + r.
Current passing through the circuit (I) = (Electrical force of cell) / (Total resistance of circuit)
Or, `I = E / (R + r)`
Or, `E = IR + Ir`
Or, `E = V + Ir`
Where, `V = IR` = Terminal potential difference of the cell.
Q. What is the electromagnetic force and loss volt in a cell?
⇒ The electromotive force of a cell: The amount of work done by an external agent in bringing a unit positive charge in a closed circuit connected to a cell is called the electromotive force of that cell.
Or, the amount of work done in bringing a unit positive charge from the negative pole to the positive pole inside a cell in an open circuit is called the electromotive force of the cell.
◼ Lost volts: Work done in bringing a unit positive charge from the negative pole to the positive pole through the active liquid inside a cell in a closed circuit is called lost volt of the cell.
Or, the amount of voltage that is lost inside the cell due to internal resistance is called the internal voltage drop or loss volt.
Q. Resistance of a conductor depends on which factors?
⇒ Resistance of a conductor depends on the following factors ------
(i) Length: The resistance of a conductor is proportional to its length (`l`) if temperature, nature of the material, and cross-sectional area (` A`) remain unchanged.
i.e., `R ∝ l` when other things are fixed.
(ii) Cross-sectional area: The resistance of a conductor is inversely proportional to its cross-sectional area (`A`), If the temperature, nature of the material and length (`l`) remain unchanged.
i.e., `R ∝ frac {1}{A}` when other things are fixed.
(iii) Nature of the material: Although the temperature, length (`l`), and cross-sectional area (` A`) are unchanged, the resistance of different conductors of different materials is different.
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| WBBSE class 10 physical science Current electricity notes. |
Q. What is resistivity? Determine the expression for resistivity.
⇒ Resistivity: The resistance of a conductor having unit length and unit cross-sectional area is called the resistivity or specific resistance of the material of that conductor.
Or, the resistance between the two opposite faces of a unit cube of a conductor is called the resistivity or specific resistance of the material of that conductor.
◼ Suppose at a definite temperature, the resistance of a conductor having length `l` and cross-sectional area `A` be R, then
ஃ `R ∝ l` when `A` is fixed and
`R ∝ frac {1}{A}` when `l` is fixed.
ஃ `R ∝ frac {l}{A}` when both `l` and `A` are variable
Or, `R = ρ frac {l}{A}`
Where `ρ` is a constant. This constant `ρ` is called the resistivity of the conductor.
Q. The value of resistivity depends on which factors?
⇒ The value of the resistivity depends on (1) the nature of the material and (2) temperature of the conductor.
Q. Write the unit and dimension of resistivity. What is meant by '' Resistivity of Copper at `20`℃ is `1.76 times 10 ^ -8 ohm.m`?
⇒ CGS unit of resistivity is `ohm. cm` and SI unit `ohm. m`.
◼ Dimension of resistivity = `[ML ^ 3T ^ -3I ^ -2]`
◼ '' Resistivity of Copper at `20`℃ is `1.76 times 10 ^ -8 ohm.m` means that at `20`℃ the resistance between the two opposite faces of a copper cube having length `1 m` and cross-sectional area `1 m^2` is `1.76 times 10 ^ -8 ohm`.
Q. What are conductance and conductivity? What is the unit of conductivity?
⇒ Conductance: Reciprocal of resistance is called conductance.
Thus, if the resistance of a conductor is R, the conductance, `K = frac{1}{R}`.
Conductivity: Reciprocal of resistivity is called conductivity.
Thus, if the resistivity of a conductor is `ρ`, then conductivity, 𝝈 = `frac {1}{ρ}`
◼ CGS unit of conductivity mho `cm ^ -1` (℧. `cm ^ -1`) `and SI unit mho. `m ^ -1` `(℧. m ^ -1)` or simens. `m ^ -1` `(S. m ^ -1)`.
Q. What is combination of resistance? How many types are there and what are they?
⇒ Combination of resistance: when more than one resistor is used together in an electrical circuit, those resistors are called combination of resistance.
◼ There are two types of combination of resistance (1) series combination and (2) parallel combination.
Q. What do you mean by equivalent resistance?
⇒ Equivalent resistance: If only one resistor can be used instead of a combination of resistance in an electrical circuit so that the total current and potential difference of the circuit remains unchanged, then that one resistor is called equivalent resistance.
Q. What is series combination of resistances? Determine the equivalent resistance of resistances connected in series. Write the characteristics of series combination of resistances.
⇒ Series cobination of resistances: When a number of resistors are connected in such a way that the last end of a resistor is connected to the first end of the next resistor and same current flows through each, then the cobination is called series cobination of resistances.
◼ Determination of equivalent resistance of resistors connected in series:
Let us consider three resistors `R_1`, `R_2` and` R_3` are connected in series between points A and D in an electrical circuit. The same current `I` flows through each resistor and the potentials at the points A, B, C and D are `V_A`,` V_B`, `V_C` and` V_D`, respectively.
ஃ According to Ohm's formula -----
`V_A` -` V_B` = `R_1 I`
Or, `V_B` - `V_C` = `R_2 I`
Or, `V_C` - `V_D` =` R_3 I`
Adding the above equations, we get
`V_A` -`V_D` = `(R_1 + R_2 + R_3) I` ------- (1)
Now, if the equivalent resistance of the combination is `R`, then
`V_A` -`V_D` = `R I` ----------- (2)
Comparing the equations (1) and (2), we get
`R = R_1 + R_2 + R_3`
Thus, equivalent resistance of resistor connected in series = the sum of the resistors in series.
◼ Characteristics of the series combination of resistance:
(i) The amount of current flowing through each resistance is equal.
(ii) Equivalent resistance of the combination is equal to the sum of all resistances.
(iii) Equivalent resistance is greater than the largest resistance of the combination.
(iv) Potential difference of the combination = sum of the potential difference of each resistance.
(v) If there are `n` number of resistance (let's say each has a value `r`) then the equivalent resistance,
`R = r + r + ------- = nr`
(vi) Since the current in a circuit is constant, the potential difference across any resistance is proportional to that resistance.
Q. What is parallel combination of resistances? Determine the equivalent resistance of resistances connected in parallel. Write the characteristics of parallel combination of resistances.
⇒ Parallel combination of resistances: If all the ends of the resistances is connected to one point and the other end is connected to another point and the potential difference between the two ends of the resistance is the same then the combination of that resistances is called parallel combination.
◼ Determination of equivalent resistance of resistors connected in parallel:
Let us consider three resistors `R_1`, `R_2` and R_3` are connected in parallel between points A and B in an electrical circuit. Since the current `I` of the circuit is divided into three resistances, so
`I = I_1 + I_2 + I_3` ------------- (1)
Now if the potential difference between points A and B is = `V`, according to Ohm's formula ----
`I_1 = frac{V}{R_1}`, `I_2 = frac{V}{R_2}` `and `I_3 = frac{V}{R_3}`
ஃ From equation (1) we get ----
`I = frac{V}{R_1} + frac{V}{R_2} + frac{V}{R_3}`
Or, `I = V ( frac{1}{R_1} + frac{1}{R_2} + frac{1}{R_3})` --------(2)
Now, if the equivalent resistance of the combination is `R`, then
`I = V times\frac{1}{R}` -----------(2)
Comparing the equations (1) and (2), we get
`frac{1}{R} = frac{1}{R_1} + frac{1}{R_2} + frac{1}{R_3}`
Thus, in parallel combination of the resistances, reciprocal of equivalent resistance = sum of the reciprocals of individual resistances.
◼ Characteristics of the parallel combination of resistance:
(i) The potential difference of each resistance is same.
(ii) The reciprocal of equivalent resistance is equal to the sum of the reciprocals of individual resistances.
(iii) Equivalent resistance is smaller than the smallest resistance of the combination.
(iv) Total current flowing through the circuit is equal to the sum of current flowing through each resistance.
(v) If there are `n` number of resistance (let's say each has a value `r`) then the equivalent resistance,
`frac{1}{R} = frac{1}{r} + frac{1}{r} + ------- = frac{n}{r}`
Thus, equivalent resistance `R = frac{r}{n}`
(vi) Since the terminal potential difference is constant, the current through any resistance is inversely proportional to that resistance.
(vii) When the resistances are interchanged, their terminal potential difference and equivalent resistance remain unchanged.
Q. Prove that the equivalent resistance of resistances in series combination is greater than the greatest resistance.
⇒ Suppose three resistances `R_1`,` R_2` and `R_3` are connected in series and ` R_1` is the greatest resistance.
Equivalent resistance of the combination, `R_s = R_1 + R_2 + R_3`
Or, `R - R_1 = R_2 + R_3` = `+ ve`
ஃ `R - R_1` > 0 Or, ` R` > `R_1`
Thus, the equivalent resistance of resistances in series combination is greater than the greatest resistance.
Q. Show that the equivalent resistance of resistances in parallel combination is smaller than the smallest resistance.
⇒ Suppose three resistances `R_1`,` R_2` and `R_3` are connected in parallel and `R_1` is the smallest resistance.
If the equivalent resistance is `R_p`, then
`frac{1}{R_p} = frac{1}{R_1} + frac{1}{R_2} + frac{1}{R_3}`
Or, `frac{1}{R_p} - frac{1}{R_1} = frac{1}{R_2} + frac{1}{R_3}`
Or, `frac{1}{R_p} - frac{1}{R_1} = +ve`
Or, `frac{1}{R_p} - frac{1}{R_1}` > 0
Or, `frac{1}{R_p}` > `frac{1}{R_1}`
Or, `R_p` < `R_1`
Thus the equivalent resistance of resistances in parallel combination is smaller than the smallest resistance.
Q. Calculate the equivalent resistance when `n` number of resistances, each of value `R`, are connected in series combination as well as in parallel combination. What is the ratio of these two values?
⇒ If `n` number of resistances, each of value `R`, are connected in series combination then the equivalent resistance,
`R_s = `R + R + ---------------------n times = nR`
Again, If they are connected in parallel combination and the equivalent resistance is `R_p`, then
`frac{1}{R_p} = frac{1}{R} + frac{1}{R} + -------n times = frac{n}{R}`
Or, `R_p = \frac{R}n`
◼ The ratio of equivalent resistances,
`\frac{R_s}{R_p} = \frac{nR}{\frac Rn} = n^2`
Q. Why are electrical appliances used in household connected to parallel combination ?
⇒ Electrical appliances used in household are connected to parallel combination because ---
(1) The terminal potential difference of each electrical device remains same. So the efficiency of the instruments remains good.
(2) If one device is switched off or does not work, it does not affect the other device.
(3) The equivalent resistance of the whole house is less.
Q.Write down Joule's laws of heating effect of current.
⇒ The Joule's laws of heating effect of current are ---
(1) First formula: If the resistance `(R)` of the conductor and the time of flow of current `(t)` remain constant, then the amount of heat produced in the conductor is directly proportional to the square of the current passed `(I)`.
i.e., `H` ∝` I ^ 2` [when `R` and` t` are constant].
(2) Second formula: If the amount of current `(I)` and the time of flow of current `(t)` remain constant, then the amount of heat produced in the conductor is directly proportional to the resistance of the conductor `(R).
i.e., `H` ∝` R` [when `I` and` t` are constant]
(3) Third law: If the resistance `(R)` of a conductor and the amount of current `(I)` are constant, then then the amount of heat produced in the conductor is directly proportional to t the time of flow of current `(t)`
i.e., `H` ∝` t` [when `R` and` I` are constant]
Combining the above laws we get,
`H` ∝` I ^ 2 R t` [when `I`, `R`, `t` all vary]
Or, `H` =` \ frac {I ^ 2Rt} J`
[Here `J` is a constant called mechanical equivalent of heat]
Or, H = `frac{I^2R t}{4.2}` cal [∵ J = 4.2 J/cal]
The law can be expressed as H = `I^2 R t` joule in `SI` system.
Q. Why is a nichrome wire used in electric heaters?
⇒ Nichrome wire is used in electric heaters because ---
(1) The resistivity of nichrome wire is very high so the resistance is high. As a result, the heat generated according to Joule's law is higher.
(2) Its melting point is high, so it will not melt so easily.
(3) It does not oxidize at high temperature.
Q. What is a fuse wire? Explain its working principle.
⇒ Fuse wire: A thin wire made up of an alloy of lead and tin that is connected to the live wire in an electrical circuit is called a fuse wire.
◼ The resistance of a fuse wire is very high and the melting point is low. Each fuse can withstand a certain maximum amount of current. When the amount of current exceeds that limit, the heat generated in the fuse wire melts the wire and disconnects the electrical circuit. In this way, it saves the electrical equipment.
Q. What is meant by a 5 A fuse?
⇒ A 5A fuse means that the fuse can withstand a maximum current of 5 A. When the current exceeds 5 A it melts and disconnects the electrical circuit.
Q. What is a short circuit?
⇒ Short circuit: When two opposite electric lines or two opposite poles of an electrical cell are connected through very low resistance, an excessive amount of current flows in the circuit. As a result, an excessive amount of heat is generated, sometimes leading to a fire in the circuit. This is called short circuit.
Q. What is electrical power? Show that electrical power `P = \frac{V^2}R`. What is the SI unit of electrical power?
⇒ Electrical power: The rate at which an electrical device performs electrical work is called the electrical power of the electrical device.
Or, the rate at which electrical energy is consumed with respect to time is called the electrical power of the electrical device.
That is electric power (P) = (electrical work / time) = `\frac {W}t`.
◼ Suppose an electrical device transmits `Q` amount of electric charge in `t` time through the potential difference `V`.
Electrical work `(W) = V Q`
Electrical power `(P) = \frac{W}t` = `\frac{VQ}t` = `\frac{VIt}t` = `V I`
Again, if the resistance of the conductor is `R` then according to Ohm's law `V = IR`
ஃ `P = VI = IR.R = I^2R = \frac{V^2}{R^2}\timesR = \frac{V^2}{R}`
◼ The SI unit of electrical power is watt.
Q. What is electrical energy? What is the unit of electrical energy in SI system?
⇒ Electric power: The efficiency and capacity of an electrical device is called its electrical power.
◼ The unit of electrical energy in the SI system is Joule (J).
Q. Write down Faraday's laws of electromagnetic induction.
⇒ Faraday's laws of electromagnetic induction:
First law: When there is a change in the magnetic flux linked with a closed coil, an emf is induced in the coil, thereby producing electric current.
Second law: The magnitude of the induced emf (emf) is directly proportional to the time rate of change of magnetic flux linked with the coil.
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