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=46Ω

Step by step solution

01

Given data 

  • i0=1A
  • i=10×10-3A
02

Understanding the concept

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

i=i0e-tτL

Formulae:

The current decay in the RL circuit is given by,

i=i0e-tτL

The inductive time constant is,

τL=LR

03

Calculate the resistance R in the circuit 

The current decay inRLcircuit is given by,

i=i0e-tτLlnii0=-tτLτL=-tlnii0

Hence,

LR=-tlnii0

10R=-1ln10×10-31.0

By solving for R,

R=46Ω

Therefore the resistance in the circuit is 46 ohm.

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