First slide

voltmeter

Question

In the circuit when switch $S_{1}$ is closed and $S_{2}$ is open, the ideal voltmeter shows a reading 18V. When switch $S_{2}$ is closed and $S_{1}$ is open, the reading of voltmeter 24V. When $S_{1}$ and $S_{2}$ both are closed the voltmeter reading will be

Moderate

A

14.4 V
B

20.6 V
C

24.2 V
D

10.8 V

Solution

When $S_{1}$ is closed $(\frac{E}{6 + r}) 6 = 18 \to (1)$
When only $S_{2}$ closed $(\frac{E}{12 + r}) 12 = 24 \to (2)$
Dividing (1) and (2) $(\frac{12 + r}{6 + r}) \frac{1}{2} = \frac{3}{4}$
$24 + 2 r = 18 + 3 r$
$r = 6 Ω$
When both are closed $\frac{6 \times 12}{18} = 4 Ω$
$\frac{V}{18} = \frac{(\frac{E}{4 + r}) 4}{(\frac{E}{6 + r}) 6} \frac{V}{6} = \frac{2 (6 + 6)}{(4 + 6)}$
$V = \frac{12 \times 12}{10} = 14 .4 V$

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