Question

In an experiment on a circuit, as shown in the figure, the voltmeter shows 8V reading. The resistance of the voltmeter is 

• A. 20Ω
• B. 320Ω
• C. 160Ω
• D. 1.44kΩ

Answer 1

The Correct Option is C

Given the values:
$I = \frac{8\ \text{volts}}{10\ \Omega} = \frac{4}{5} = 0.8\ \text{A}$

Voltage across $5\ \Omega$: 
$V_1 = (0.8) \times 5 = 4\ \text{volts}$ 

Hence, the electromotive force (e.m.f) of the battery is equal to the voltage across $10\ \Omega$, which is:

$\text{EMF} = 8 + 4 = 12\ \text{volts}$

Therefore, the correct option is: (C): 160$\ \Omega$

Answer 2

In the given circuit experiment, the voltmeter shows a reading of $8\ \text{V}$. Suppose the total current flowing through the circuit is: 

$I = \frac{\text{EMF}}{R_{\text{total}}} = \frac{12\ \text{V}}{10\ \Omega + R_v}$

The voltmeter is connected across a $R = 10\ \Omega$ resistor and measures $8\ \text{V}$. Let the resistance of the voltmeter be $R_v$.

From Ohm’s Law, the current through the $10\ \Omega$ resistor is: 
$I = \frac{8}{10} = 0.8\ \text{A}$

The same current flows through the voltmeter branch. The voltage across the voltmeter is also $8\ \text{V}$, so we use: 
$R_v = \frac{8}{0.05} = 160\ \Omega$

Therefore, the resistance of the voltmeter is: 160 $\Omega$ 
Correct Option: (C)