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Chapter 30: Q51P (page 899)

The current in an RL circuit drops from1.0 A to 10 mA in the first second following removal of the battery from the circuit. If L is10 H, find the resistance R in the circuit.

Short Answer

Expert verified

R=46惟

Step by step solution

01

Given data 

  • i0=1A
  • i=10脳10-3A
02

Understanding the concept

When the source of constant emf is removed, the current decays from a valueaccording to,

i=i0e-t蟿L

Formulae:

The current decay in the RL circuit is given by,

i=i0e-t蟿L

The inductive time constant is,

蟿L=LR

03

Calculate the resistance R in the circuit 

The current decay inRLcircuit is given by,

i=i0e-t蟿Llnii0=-t蟿L蟿L=-tlnii0

Hence,

LR=-tlnii0

10R=-1ln10脳10-31.0

By solving for R,

R=46惟

Therefore the resistance in the circuit is 46 ohm.

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How long would it take, following the removal of the battery, for the potential difference across the resistor in an RL circuit (with L = 2.00H, R = 3.00) to decay to 10.0% of its initial value?
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