# GATE 2015 EE – SET 2 – Question 8

Solution:

100$$\pi$$RC = 50

R= $$\frac{50}{100\pi c}$$

During positive half cycle

$$V_{0}$$  = $$\frac{V_{in}(R)}{(R-jX_{c})}$$ , where R = 50$$X_{c}$$

$$V_{0}$$ = $$\frac{v_{in}R}{R-jX_{c}}$$ = $$\frac{v_{in}(50X_{c})}{-jX_{c}}$$

$$V_{0}$$ = $$\frac{100sin(100\pi t)50X_{c}}{50X_{c}-jX_{c}}$$

Positive half cycle \Rightarrow $$V_{0}(peak)$$ = $$\left | 100 \right |$$

Negative half cycle \Rightarrow $$V_{0}(peak)$$ = $$\left | -100 \right |$$

$$V_{0}$$ = $$\left | 100 \right |$$ + $$\left | -100 \right |$$ = 200 V