Question

A $RLC$ circuit is in its resonance condition. Its circuit components have value $R=5\Omega ,L=2H,C=0.5mF,V=250V.$Then find the power in the circuit

• A. $6kW$
• B. $10kW$
• C. $12kW$
• D. $12.5kW$

Answer 1

The correct option is D

$12.5kW$

Step 1. Given Data,

Rasistance $R=5\Omega$

Inductance $L=2H$

Capacitor $C=0.5mF$

Voltage $V=250V.$

Step 2. We have to calculate the power in the circuit,

We know that for $RLC$ circuit,

$X_L=X_C$

Therefore, Impedence $Z=R$

We know that,

$$\begin{gathered} i_{rms}=\frac{V}{Z} \\ \Rightarrow i_{rms}=\frac{V}{R} \end{gathered}$$

We know that Power $\mathit{P}$ is,

$$\begin{gathered} P={(i_{rms})}^2\times R \\ \Rightarrow P={\left(\frac{V}{R}\right)}^2\times R=\frac{V^2}{R} \\ \Rightarrow P=\frac{250\times 250}{5} \\ \Rightarrow P=12500J/S \\ \Rightarrow P=12.5KW \end{gathered}$$

Therefore, the power in the circuit is $P=12.5kW$,

Hence, the correct option is $\text{'}D\text{'}$