Q18 of 126 Page 198

The potential difference between the terminals of a 6.0 V battery is 7.2 V when it is being charged by a current of 2.0 A. What is the internal resistance of the battery?

0.6Ω

Given,


The potential difference across the setup, V= 7.2V


The emf of the cell, E=6V


The current flowing through the circuit, i= 2A


Formula used:


When the battery is charging the potential difference, V across the cell can be written as,



Where ‘E’ is the emf of the cell and ‘r’ is internal resistance of the cell.


Solution:


As the battery is getting charged, the internal resistance can be calculated from the eqn.1, as



And by substituting the given values,



Hence the internal resistance of the cell is 0.6Ω


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Figure shows an arrangement to measure the emf ϵ and internal resistance r of a battery. The voltmeter has a very high resistance and the ammeter also has some resistance. The voltmeter reads 1.52 V when the switch S is open. When the switch is closed the voltmeter reading drops to 1.45 V and the ammeter reads 1.0 A. Find the emf and the internal resistance of the battery.


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The potential difference between the terminals of a battery of emf 6.0 V and internal resistance 1 Ω drops to 5.8 V when connected across an external resistor. Find the resistance of the external resistor.

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The internal resistance of an accumulator battery of emf 6 V is 10 Ω when it is fully discharged. As the battery gets charged up, its internal resistance decreases to 1Ω. The battery in its completely discharged state is connected to a charger which maintains a constant potential difference of 9V. Find the current through the battery

(a) just after the connections are made and


(b) after a long time when it is completely charged.


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Find the value of i1/i2 in figure if (a) R = 0.1Ω, (b) R = 1 Ω (c) R = 10 Ω. Note from our answers that in order to get more current from a combination of two batteries they should be joined in parallel if the external resistance is small and in series if the external resistance is large as compared to the internal resistances.