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Question : 27
Total: 27
(a) Describe briefly, with the help of a circuit diagram, the method of measuring the internal resistance of a cell.
(b) Give reason why a potentiometer is preferred over a voltmeter for the measurement of emf of a cell.
(c) In the potentiometer circuit given below, calculate the balancing lengthl 5 V 2 V
OR
(a) State the working principle of a meter bridge used to measure an unknown resistance.
(b) Give reason
(i) Why the connections between the resistors in a metre bridge are made of thick copper strips,
(ii) Why is it generally preferred to obtain the balance length near the mid-point of the bridge wire.
(c) Calculate the potential difference across the4 Ω
(b) Give reason why a potentiometer is preferred over a voltmeter for the measurement of emf of a cell.
(c) In the potentiometer circuit given below, calculate the balancing length
OR
(a) State the working principle of a meter bridge used to measure an unknown resistance.
(b) Give reason
(i) Why the connections between the resistors in a metre bridge are made of thick copper strips,
(ii) Why is it generally preferred to obtain the balance length near the mid-point of the bridge wire.
(c) Calculate the potential difference across the
Solution:
Circuit diagram and describing the method to measure internal resistance of cell by potentiometer
Reason
Calculating balancing length and reason (circuit works or not)
(a) Circuit diagram :
K 1 K 2 l 1
E = K l 1
With the keyK 2 l 2
V = K l 2
r = (
− 1 ) R
r = (
− 1 ) R
(b) The potentiometer is preferred over the voltmeter for measurement of e.m.f. of a cell because potentiometer draws no current from the voltage source being measured.
(c)V = 5 V , R A B = 50 Ω , R = 450 Ω
I =
=
= 0.01 A
V A B = 0.01 × 50 = 0.5 V
K =
= 0.05 Vm − 1
l =
=
= 6 m
With2 V
I =
= 0.04 A .
Potential difference acrossAB = 0.004 × 50 = 200 mV
OR
(a) The circuit diagram of the metre bridge is as shown below:
Working Principle: The working principle of the meter bridge is the same as that of a Wheatstone bridge. The Wheatstone bridge gets balanced when:
=
For the metre bridge, circuit shown above, this relation takes the form
=
Determination of unknown Resistance( R ) S
We find the value of the balancing lengthl 1 S
=
to calculateR
By choosing (at least three) different values ofS R R
(b) (i) This is to ensure that the connections do not contribute any extra, unknown, resistances in the circuit.
(ii) This is done to minimize the percentage error in the value of the unknown resistance.
Alternatively, This is done to have a better "balancing out" of the effects of any irregularity or non-uniformity in the metre bridge wire.
(c) This can help in increasing the sensitivity of the metre bridge circuit.
Apply the current junction rule of Kirchhoff's Law at pointD
i = i 1 + i 2
Apply Kirchhoff's Voltage rule for the mesh AEFBA
4 i + 2 i 1 = 8
or,2 i + i 1 = 4
Apply Kirchhoff's voltage rule for mesh DEFCD
4 i + 1 i 2 = 6
or, 4 i + i 2 = 6
Adding equation (ii) and (iii), we get
6 i + i 1 + i 2 = 10
or, 6 i + i = 10 [using equation (i)]
or i =
A
Now, the potential difference across resistor4 Ω
V E F = i × 4
=
× 4
= 5
V
Reason
Calculating balancing length and reason (circuit works or not)
(a) Circuit diagram :
Brief description: Plug in the key
With the key
(b) The potentiometer is preferred over the voltmeter for measurement of e.m.f. of a cell because potentiometer draws no current from the voltage source being measured.
(c)
With
Potential difference across
OR
(a) The circuit diagram of the metre bridge is as shown below:
Working Principle: The working principle of the meter bridge is the same as that of a Wheatstone bridge. The Wheatstone bridge gets balanced when:
For the metre bridge, circuit shown above, this relation takes the form
Determination of unknown Resistance
We find the value of the balancing length
to calculate
By choosing (at least three) different values of
(b) (i) This is to ensure that the connections do not contribute any extra, unknown, resistances in the circuit.
(ii) This is done to minimize the percentage error in the value of the unknown resistance.
Alternatively, This is done to have a better "balancing out" of the effects of any irregularity or non-uniformity in the metre bridge wire.
(c) This can help in increasing the sensitivity of the metre bridge circuit.
Apply the current junction rule of Kirchhoff's Law at point
Apply Kirchhoff's Voltage rule for the mesh AEFBA
or,
Apply Kirchhoff's voltage rule for mesh DEFCD
Adding equation (ii) and (iii), we get
Now, the potential difference across resistor
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