Chapter 23, Problem 48A

(a)

To determine

The change in electric potential energy as charge goes around the circuit many times.

Whether the law of conservation of energy holds or not.

Explanation of Solution

Given:

A battery having voltage V is connected in a circuit. There are two branches in the circuit. First branch has two resistors $R_1$ and $R_2$ connected in series while third branch contains 1 resistor $R_1$ in parallel connection with first branch.

Formula Used:

As per Kirchhoff’s loop rule, $\sum V=0$

Calculations:

The change in electric potential energy $=q\Delta V$

Since $\sum V=0$ as per Kirchhoff’s loop rule, the change in potential energy would be zero when charge goes around in the circuit multiple times. As there is no change in the electric potential energy, the law of conservation of energy holds true.

(b)

To determine

The way there would be change in energy as charge goes around the circuit many times if the Kirchhoff’s loop rule was not true.

Explanation of Solution

Given:

A battery having voltage V is connected in a circuit. There are two branches in the circuit. First branch has two resistors $R_1$ and $R_2$ connected in series while third branch contains 1 resistor $R_1$ in parallel connection with first branch.

Formula Used:

As per Kirchhoff’s loop rule, $\sum V=0$

Calculations:

The change in electric potential energy $=q\Delta V$

If Kirchhoff’s loop rule was not true, then the energy of the charge would have continuously decreased during each round in the loop and eventually current would be zero.