Question

A cell of emf 2 V and internal resistance 1 ohm is connected to a conductor whose volt-ampere relation is given by $V^2=\alpha I$ where $\alpha$ is a constant and is equal to $100$ . Find the current drawn from the cell.

• A. $10mA$
• B. $40mA$
• C. $50mA$
• D. $20mA$

Answer 1

Answer: (B)

$40mA$

Let current flowing through the circuit be $i$.

Then, potential difference across the conductor is

$v=\epsilon -iR$

$v=2-i$

From the question, $i=\frac{v^2}{\alpha }=\frac{v^2}{100}$

$⟹v^2+100v-200=0$

Solving, $v=\frac{-100\pm \sqrt{{10}^4+800}}{2}=-50\pm 30\sqrt{3}=-50\pm 51.96$

Since a conductor cannot produce current, voltage drop cannot be negative across it.

Hence, $v\approx 2$

Current is given by: $i=\frac{v^2}{\alpha }=40mA$