Question

In the circuit shown below, each battery is 5V and has an internal resistance of 0.2 ohms.

The reading of the voltmeter is:
A) zero
B) 5V
C) 10V
D) 20V

Answer 1

Hint : We need to find the net EMF of the circuit considering that all the EMFs are connected such that they support each other. The net resistance of the circuit can be calculated considering that all the resistors are connected in series. The voltmeter will measure the potential difference of the EMF that connects the points A and D.

Formula Used: In this solution we will be using the following formula,
 $ V = IR $ where $ V $ is the voltage $ I $ is the current and $ R $ is the resistance.

Complete step by step answer
In the circuit given to us, all the cells are connected in series such that they are all supporting each other, that is, their opposite ends are connected together. In this configuration, the net EMF in the circuit will add up. There will be a flow of current in the circuit which will cause a potential drop across the cell connecting points AD which will be measured in the voltmeter. Let's measure the current flowing in the circuit first.
The net EMF of the circuit will be the sum of the EMFs of all the cells i.e.
 $ E = 8 \times 5 $
 $ \Rightarrow E = 40\,V $
Since all the cells have an identical internal resistance of $ 0.2\,\Omega $ , the total resistance considering all of them are connected in series will be
 $ R = 8 \times 0.2 $
 $ \Rightarrow R = 1.6 $
The current in the circuit can then be determined by ohm’s law which tells us
 $ V = IR $
Since $ V = E = 40\,V $ and $ R = 1.6\,\Omega $ , we can calculate $ I $ as
 $ I = \dfrac{V}{R} $
 $ \Rightarrow I = \dfrac{{40}}{{1.6}} = 25\,A $
The voltmeter will measure the potential difference across the battery that connects points AD which can be calculated as the difference of the EMF of the cell and the potential drop that occurs across the internal resistance of the cell:
 $ {E_{AD}} = E - Ir $
 $ {E_{AD}} = 5 - (25)(0.2) $
So on calculating we get,
$ \Rightarrow {E_{AD}} = 0 $ which corresponds to option (A).

Note
Here we have assumed the voltmeter to be an ideal voltmeter which means it will have infinite resistance and no current will flow through the resistor. While calculating the net EMF of the circuit, we must take into account whether the cells are supporting or opposing each other by looking at the connections of their terminals properly.