Question

An inductor $2/\pi$ F and a resistor $100/\pi$ are connected in series across a source of emf v=$10$sin $100$ [$\pi$ t]. Here t is in second. (a) find the impedance of the circuit find the energy dissipated in the circuit in $20$ minutes.

Answer 1

We know that, impedance of a LR circuit is $Z=\sqrt{R^2+{\omega }^2{L}^2}$---- (1)

emf, V=$10sin100\pi t$

$\omega =2\pi f=100\pi f=50Hz$

Therefore, $\omega L=2\pi fL=2\times 50\times \pi \times \frac{2}{\pi }\omega L=2\times 50\times 2=200$

(1)=.>$Z=\sqrt{{\left(\frac{100}{\pi }\right)}^2+{200}^2}$

=202 ohm

Hence impedance of the circuit, Z= 202 ohm