Question

In adjacent circuit the instantaneous current equation is–

• A. 2 sin $\left( 100t - \frac{\pi}{4} \right)$
• B. $\sqrt{2}$sin $\left( 100t - \frac{\pi}{4} \right)$
• C. $\sqrt{2}$sin$\left( 200t - \frac{\pi}{4} \right)$
• D. $\sqrt { 2 }$ $\left( 100t + \frac{\pi}{4} \right)$

Answer 1

Answer: (B)

$\sqrt{2}$sin $\left( 100t - \frac{\pi}{4} \right)$

Answer 2

Let f is the phase difference between V and i

tan f = $\frac{X_{L}}{R}$= $\frac{\omega L}{R}$ = $\frac{100 \times 1}{100}$ = $\frac{\pi}{4}$

From diagram it is clear that i lags with V

\ Instantaneous current equation will be

i₀ = sin (100 t –f) where f = $\frac{\pi}{4}$ and i₀ = $\frac{V_{0}}{Z}$

= $\frac{V_{0}}{\sqrt{R^{2} + (\omega L)^{2}}}$ = $\frac{200}{\sqrt{(100)^{2} + (100 \times 1)^{2}}}$ = $\sqrt{2}$

\ i = $\sqrt{2}$ sin (100 t – $\frac{\pi}{4}$)