GATE 2015 EE – SET 2 – Question 45

Solution :

$$V_{P}$$ = ± 15 V ,T = 0.4$$\pi $$ms ,R=5Ω , L = 10 * 10^{-3}H , C + 4 * 10^{-6}F , w = 5000 rad/sec , $$(V_{c})_{P}$$ = ?

Fourier series of a square wave ,

$$\sum_{n= 1,3,5}^{\infty } \frac{4V}{n\pi } sin\omega t$$

$$\sum_{n= 1,3,5}^{\infty } \frac{4(15)}{n\pi } sin\omega t$$

$$\sum_{n= 1,3,5}^{\infty } \frac{19.10}{n\pi } sin\omega t$$

$$X_{c}$$ = $$\frac{1}{w{c}}$$ = $$\frac{1}{5000*4*10^{-6}}$$ = 50 Ω

$$X_{c}$$ =WL = 5000 *10 * $$10^{-3} $$= 50Ω

$$X_{c}$$  = $$X_{L}$$ = ckt is in resonance

$$V_{c}$$= $$I_{fundamental}*X_{c}*Sin\omega t$$

$$V_{c}$$ =$$ \frac{V_{fundamental}}{R} * X_{c} Sin\omega t$$

$$V_{c}$$ =$$\frac{19.10}{5} * 50 Sin\omega t$$
$$V_{c}$$ = $$191 Sin\omega t$$

Amplitude of$$ V_{c}$$ = 191V