A 6.0-V battery that can store $500.0 \mathrm {~J}$ of energy is connected to a resistor. How much charge must flow between the battery's terminals to completely drain the battery if it is fully charged? Assume that the voltage of the battery remains the same until it is totally drained.
A) 83 C
B) 0.010 C
C) 3000 C
D) 0.07 C

Question

Quizplus · Accepted Answer

The equation for the energy stored in a battery is:
$$ E = VQ $$
where E is the energy stored, V is the voltage, and Q is the charge that flows between the battery's terminals. We can rearrange this equation to solve for Q:
$$ Q = \frac{E}{V} $$
Plugging in the given values, we get:
$$ Q = \frac{500.0 \mathrm{~J}}{6.0 \mathrm{~V}} = 83.33 \mathrm{~C} $$
Since charge is quantized in units of the elementary charge (1.60 x 10^-19 C), we round our answer to the nearest multiple of this quantity, which gives us the final answer of:
$$ Q = 83 \mathrm{~C} $$

A 60-V Battery That Can Store 500.0 J500.0 \mathrm {~J}500.0 J Of Energy Is Connected to a Resistor

A 60-V Battery That Can Store $500.0 \mathrm {~J}$ Of Energy Is Connected to a Resistor