The output $V_{0}$ in the following circuit is same as the input( $- V_{i}$ ), then the value of R would be _______ $k Ω$

4

Open in App

Solution

The correct option is A 4
Applying KVL at node-1, we get

$\frac{V - V_{0}}{2} + \frac{V - V_{i}}{R} + \frac{V - V_{i}}{2 R} + . . . \frac{V - V_{i}}{n R} = 0$

$∵ V_{0} = - V_{i}$

$\Rightarrow - (\frac{V + V_{i}}{2}) = \frac{V - V_{i}}{R} + \frac{V - V_{i}}{2 R} + \dots + \frac{V - V_{i}}{n R}$

$Due to virtual ground, V = 0$

$\Rightarrow \frac{- V_{i}}{2} = \frac{- V_{i}}{R} (1 + \frac{1}{2} + \frac{1}{4} + . . . + \frac{1}{n})$
$\frac{R}{2} = (1 + \frac{1}{2} + \frac{1}{4} + . . . + \frac{1}{n})$
$∵ 1 + \frac{1}{2} + \frac{1}{4} + . . . + \frac{1}{n}$ $\to$ Sum of infinite G.P. with $a = 1$ and $r = 1 / 2$
$∴ \frac{R}{2} = \frac{1}{1 - \frac{1}{2}}$
$\Rightarrow R = 4 k Ω$

Suggest Corrections

Similar questions

Ω

V_{0}

V_{i} = 5 + 2 s i n (ω t)

V_{0}

V_{i} = 5 + 2 sin (ω t)

V_{0}

v_{i} = V_{p} c o s (t / R C)

V_{0}

V_{i} = [2 + s i n (100 t)]

V_{0}

Join BYJU'S Learning Program