The resistance of wire AB as shown in the figure is \( 12000 \, \Omega \) and \( 220 \, \text{V} \) of potential difference is applied across it. Resistance of voltmeter \( V \) is \( 6000 \, \Omega \). The point C is at one-fourth distance from the point A. What is the reading of the voltmeter?
Show Hint
The potential divider rule can be used to calculate the voltage across a component in a series circuit. The voltage is proportional to the resistance of the component.
Step 1: Understanding the Circuit.
The resistance of the wire AB is \( 12000 \, \Omega \), and a potential difference of \( 220 \, \text{V} \) is applied across it. The voltmeter with a resistance of \( 6000 \, \Omega \) is connected between point A and point C. Point C is at one-fourth the distance from point A. Thus, the resistance between point A and point C is \( \frac{1}{4} \) of the total resistance \( R_{\text{AB}} \).
Step 2: Calculating the Resistance Between A and C.
The resistance between points A and C is:
\[
R_{\text{AC}} = \frac{1}{4} \times 12000 \, \Omega = 3000 \, \Omega
\]
Step 3: Applying the Potential Divider Rule.
The voltage across the resistance \( R_{\text{AC}} \) can be found using the potential divider rule. The total resistance in the circuit is the sum of \( R_{\text{AC}} \) and the voltmeter resistance \( R_V \):
\[
R_{\text{total}} = R_{\text{AC}} + R_V = 3000 \, \Omega + 6000 \, \Omega = 9000 \, \Omega
\]
The voltage across the voltmeter is then:
\[
V_{\text{V}} = \frac{R_V}{R_{\text{total}}} \times 220 = \frac{6000}{9000} \times 220 = \frac{2}{3} \times 220 = 146.67 \, \text{V}
\]
Step 4: Conclusion.
Thus, the reading of the voltmeter is approximately \( 146.67 \, \text{V} \).
