Chapter 22, Problem 2FC

To determine

The rank of setups in descending order according to the work done by hand.

Answer to Problem 2FC

The correct option is (e) C, B, A.

Explanation of Solution

Given data:

The resistance of bulb A is $240\Omega$.

The resistance of bulb B is $192\Omega$.

The resistance of bulb C is $144\Omega$.

Formula used:

Write the expression for power $\left(P\right)$.

$P=\frac{V^2}{R}$ (1)

Here,

V is voltage, and

R is resistance.

Explanation:

The work done by hand in conducting rail is identical to the energy dissipated in the bulb. Since the time is equal for each bulb, the energy dissipated by bulb is equal to the power that is used by bulb. Hence, the work done has a proportionate change with the change in power used by bulb. The greater power usage of bulb results in a greater work done by hand.

Modify the equation (1).

$P\propto \frac{1}{R}$

Here,

V is constant.

Thus, the power used by bulb has an inverse proportional change with the change in resistance. The small resistance causes the greater power usage, whereas the high resistance results in a low power usage.

The bulb C has the lowest resistance and possesses greatest power usage.

The bulb B has second lowest resistance and possesses the second greatest power usage.

The bulb A has highest resistance and possesses lowest power usage.

Hence, the rank of powers from highest to smallest is,

$P_{\text{C}}>P_{\text{B}}>P_{\text{A}}$

Here,

$P_{\text{A}}$ is power used by bulb A,

$P_{\text{B}}$ is power used by bulb B, and

$P_{\text{C}}$ is power used by bulb C.

Similarly the rank of work done by hand from largest to smallest is,

$W_{\text{C}}>W_{\text{B}}>W_{\text{A}}$

Here,

$W_{\text{A}}$ is work done by hand in bulb A arrangement,

$W_{\text{B}}$ is work done by hand in bulb B arrangement, and

$W_{\text{C}}$ is work done by hand in by bulb C arrangement.

Conclusion:

Thus, the correct option is (e) C, B, A.