Question

An L-C-R series circuit consists of a resistance of 10 $\Omega$ a capacitor of reactance 6.0 $\Omega$ and an inductor coil. The circuit is found to resonate when put across a 300 V, 100 Hz supply- The inductance of coil is (take $\pi$ = 3)

• A. 0.1 H
• B. 0.01 H
• C. 0.2 H
• D. 0.02 H

Answer 1

Answer: (A)

0.1 H

Answer 2

Angular velocity, ${{\omega }_{0}}=2\pi \,n=2\pi \times 100$ ${{\omega }_{0}}=2\times 3\times 100=600\,rad/s$ $(\because \pi =3)$ Further ${{\omega }_{0}}=\frac{1}{\sqrt{LC}}$ ... (i) Also ${{X}_{C}}=\frac{1}{C{{\omega }_{0}}}=60\,\Omega$ $\Rightarrow$ $C=\frac{1}{{{\omega }_{0}}\times 60}=\frac{1}{600\times 60}$ $\Rightarrow$ $C=\frac{1}{36\times {{10}^{3}}}F$ So, put values in E (i), we get $600=\frac{1}{\sqrt{L\left( \frac{1}{36\times {{10}^{3}}} \right)}}$ $36\times {{10}^{4}}=\frac{36\times {{10}^{3}}}{L}$ $\Rightarrow$ $L=\frac{36\times {{10}^{3}}}{36\times {{10}^{4}}}=\frac{1}{10}=0.1H$