Question

The current I through a rod is given by $I=0.2V^{1/2}$, where V is the potential difference across it. The rod is connected in series with a resistance across a 6V battery of negligible internal resistance. What is the value of resistance such that the power dissipated in the rod is three times that dissipated in the resistor?

• A. $5\Omega$
• B. $3.535\Omega$
• C. $1.0\Omega$
• D. $2\Omega$

Answer 1

The correct option is B $3.535\Omega$

$6-IR=V$
$I=0.2V^{1/2}$
$P_{rod}=6I-I^{2}R=3I^{2}R$
$\Rightarrow IR=1.5$
$R=3.53$