An ammeter and a voltmeter are connected in series to a battery of emf E=6.0V. When a certain resistance is connected in parallel with the voltmeter, the reading of the voltmeter decreases two times, whereas the reading of the ammeter increases the same number of times. Find the voltmeter reading after the connection of the resistance.

An ammeter and a voltmeter are connected in series to a battery of emf $E = 6.0 V .$ When a certain resistance is connected in parallel with the voltmeter, the reading of the voltmeter decreases two times, whereas the reading of the ammeter increases the same number of times. Find the voltmeter reading after the connection of the resistance.

A
13 volt
B
2 volt
C
8 volt
D
23 volt

Solution:

Let $R =$ resistance of ammeter

Potential difference across voltmeter $= 6$ - potential difference across ammeter

In first case,

$V = 6 - i R$

In second case,

$\frac{V}{2} = 6 - (2 i) R$

Solving these two equations, we get

$V = 4 volt$

$V / 2 = 2 volt$

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