Question

A generator with an adjustable frequency of oscillation is connected to resistance, $R=100\Omega$, inductance $L_1=1.7mL$ and $L_2=2.3mH$ and capacitances, $C_1=4\mu F,C_2=2.5\mu F$ and $C_3=3.5\mu F$. The resonant angular frequency of the circuit is

• A. $0.5rad/s$
• B. $0.5\times {10}^{4}rad/s$
• C. $2rad/s$
• D. $2\times {10}^{-4}rad/s$

Answer 1

The correct option is B $0.5\times {10}^{4}rad/s$

In the given figure, the inductors are in parallel and the capacitors are also in parallel.

So

$\frac{1}{L_{eq}}=\frac{1}{1.7}+\frac{1}{2.3}$

$L_{eq}=0.978\times {10}^{-3}H$

$C_{eq}=4+3.5+2.5$

$C_{eq}=10\mu F=10\times {10}^{-6}F$

Resonant frequency $f=\frac{1}{2\pi \sqrt{LC}}$

$=\frac{1}{2\times 3.14\sqrt{9.78\times {10}^{-9}}}$

$=0.5\times {10}^{4}rad/s$