Consider the `RL` circuit in Fig. When the switch is closed in position `1` and opens in position `2`, electrical work must be performed on the inductor and on the resistor. The energy stored in the inductor is for the resistor energy appears as heat.
a. What is the ratio of `P_(L)//P_(R )` of the rate at which energy is stored in the inductor to the rate at which energy is dissipated in the resistor?
b. Express the ratio `P_(L)//P_(R )` as a function of time.
c. If the time constant of circuit is `t`, what is the time at which `P_(L) = P_(R )`?

Explanation

To solve the given problem step by step, we will analyze the RL circuit and derive the required ratios and expressions.

### Step-by-Step Solution

**Step 1: Power in the Resistor (P_R)**
The power dissipated in the resistor can be expressed using Ohm's law:
\[ P_R = I^2 R \]
where \( I \) is the current flowing through the resistor and \( R \) is the resistance.
...