Question

The total charge a battery can supply is rated in mA⋅h, the product of the current (in mA) and the time (in h) that the battery can provide this current. A battery rated at 1000 mA⋅hr can supply a current of 1000 mA for 1.0 h, 500 mAcurrent for 2.0 h, and so on. A typical AA rechargeable battery has a voltage of 1.2 V and a rating of 1800 mA⋅h. For how long could this battery drive current through a long, thin wire of resistance 28 Ω ?

Answer 1

Voltage, \(V=1.2 \mathrm{~V}\) Resistance, \(R=28 \Omega\)

Applying Ohm's law,

Voltage, \(V=I R\)

$$ \begin{aligned} \text { Current, } I &=\frac{V}{R} \\ &=\frac{1.2}{28} \\ &=0.0428 \mathrm{~A} \\ \text { Rate } &=1800 \mathrm{mAh} \\ \text { Time taken, } t &=\frac{1800 \times 10^{-3}}{0.0428} \\ &=42 \mathrm{hr} \\ &=151200 \mathrm{~s} \end{aligned} $$