Question

A 9.0-V battery is connected to a resistor so that there is a 0.50-A current through the resistor.For how long should the battery be connected in order to do 160 J of work while separating charges?Express your answer to two significant figures and include the appropriate units.

Answer 1

Answer:

35.6 s

Explanation:

The power through the resistor is given by:

$P=VI$

where V=9.0 V is the voltage and I=0.50 A is the current. Substituting into the formula, we find

$P=(9.0 V)(0.5 A)=4.5 W$

The power is also equal to:

$P=\frac{W}{t}$

where W is the work done while t is the time taken. Since we know the work done, W=160 J, we can re-arrange the equation to find the time taken:

$t=\frac{W}{P}=\frac{160 J}{4.5 W}=35.6 s$