Question

a 9.0 - v battery is connected to a resistor so that there is a 0.50 - a current through the resistor. part a for how long should the battery be connected in order to do 160 j of work? express your answer in seconds.

Explanation:

Step1: Recall power - work relationship

Power $P=\frac{W}{\Delta t}$, and also $P = VI$. So $W=VI\Delta t$.

Step2: Rearrange for $\Delta t$

We want to find $\Delta t$, so $\Delta t=\frac{W}{VI}$.

Step3: Substitute given values

Given $W = 160\ J$, $V=9.0\ V$, and $I = 0.50\ A$. Then $\Delta t=\frac{160}{9.0\times0.50}$.

Step4: Calculate $\Delta t$

$\Delta t=\frac{160}{4.5}\approx35.6\ s$.

Answer:

$35.6\ s$