Question

A 3 V dc supply with an internal resistance of 2$\Omega$ supplies a passive non- linear resistance characterized by the relation $V_{NL}=I_{NL}^2.$ The power dissipated in the non linear resistance is

• A. 1.0 W
• B. 1.5 W
• C. 2.5 W
• D. 3.0 W

Answer 1

The correct option is A 1.0 W


$V_{NL}=I_{NL}^2.$ ... (i)

$V_{NL}=E-I_{NL}.R$

where, E = 3V

and R = 2 $\Omega$

$V_{NL}=3-2I_{NL}=I_{NL}^2$

$I_{NL}^2+2I_{NL}-3=0$

$I_{NL}=-3Aor1A$

-3 A is rejected, because the non- linear resistor is passive and the only active element in the circuit is 3 V DC supply. Which is supplying the power to the resistor .

$So,I_{NL}=1A$

Power dissipated in the non-linear resistor

$=V_{NL}{I}_{NL}=I_{NL}^2{I}_{NL}$

$=I_{NL}^3=1^3=1W$