An inductor-resistance -battery circuit is switched on at t = 0. If the emf of the battery in one time constant tau.

Explanation

To solve the problem of finding the charge that passes through the battery in one time constant \( \tau \) in an LR circuit, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Circuit**: We have an LR circuit consisting of an inductor (L), a resistor (R), and a battery with an emf (E). When the circuit is switched on at \( t = 0 \), the current starts to increase.

2. **Current Equation**: The current \( I(t) \) in the circuit as a function of time is given by:
\[
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