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For a series \( RL \) circuit switched onto a constant voltage, the current approaches its final value with time constant

  • A.\( 1/RL \)
  • B.\( L/R \)
  • C.\( R/L \)
  • D.\( RL \)

Answer: B

Kirchhoff's law gives \( L\,di/dt + Ri = V \), a linear equation whose solution is

\[ i \;=\; \frac{V}{R}\left(1 - e^{-Rt/L}\right). \]

The exponent must be dimensionless, so the time constant is \( L/R \). Its reciprocal has units of inverse time and is the decay rate rather than the time constant

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