Question

Veena's car radio will run from a 12 V car battery that produces a current of 0.20 A even when the car engine is turned off. The car battery will not longer operate when it has lost $1.2\times {10}^{6}J$ of energy. If Veena gets out of the car, leaving the radio on by mistake, how long will it take for the car battery to go completely dead, i.e., lose all energy?

Answer 1

Given: Veena's car radio will run from a $12V$ car battery that produces a current of $0.20A$ even when the car engine is turned off. The car battery will not longer operate when it has lost $1.2\times {10}^{6}J$ of energy.

To find how long will it take for the car battery to go completely dead, i.e., lose all energy

Solution:

According to the given criteria,

$V=12V,I=0.2A,\text{Energy lost}=1.2\times {10}^{6}J$

Th formula used is,

$\text{Energy lost}=I^{2}Rt$

but according to Ohm's law,

$V=IR$

Hence, $\text{Energy lost}=VIt⟹1.2\times {10}^6=12\times 0.2\times t⟹t=\frac{1.2\times {10}^6}{2.4}⟹t=0.5\times {10}^{6}sec$

$1\text{day}=24hr=24\times 60\text{minutes}=(24\times 60\times 60)sec⟹1\text{day}=86400sec$

So $t=\frac{5\times {10}^5}{86400}\text{days}⟹t=5.79\text{days}$.

hence it will take $5.8$ days for the car battery to go completely dead, i.e., lose all energy.