A hot wire voltmeter measures the voltage across the inductor, the capacitor and the resistor as 150 V, 100 V and 50 V across a series, LCR circuit. If resistance is 100Ω , the current in the circuit is:

The correct option is 0.5 A.

Step-by-Step Explanation:

We are given a series LCR (Inductor-Capacitor-Resistor) circuit where the voltages across the individual components are measured using a hot wire voltmeter. A hot wire voltmeter measures the root mean square (rms) value of the alternating voltage.

Let:
Voltage across the inductor, $V_L=\; 150\text{V}$
Voltage across the capacitor, $V_C=\; 100\text{V}$
Voltage across the resistor, $V_R=\; 50\text{V}$
Resistance of the resistor, $R=\; 100\Omega$

In a series LCR circuit, the same current flows through the inductor, capacitor, and resistor. Therefore, the rms current in the circuit, $I$, can be directly calculated using Ohm's law applied across the resistor:

$I=\frac{V_R}{R}$

Substituting the given values into the equation:

$I=\frac{50\text{V}}{100\Omega }$

$I=\; 0.5\text{A}$

Thus, the current in the circuit is 0.5 A, which corresponds to the correct option.