Physics · Electromagnetic induction: Faraday's law, induced emf and current, Lenz's law, eddy currents, self and mutual inductance
A coil of self inductance and resistance is connected through a switch to a batt
A coil of self inductance \( 10 m H \) and resistance \( 0.1 \Omega \) is connected through a switch to a battery of internal resistance \( 0.9 \Omega \) After the switch is closed, the time taken for the current to attain \( 80 \% \) of the saturation value is : (Take \( l n 5=1.6) \)
- A. \( 0.103 s \)
- B. \( 0.016 s \)
- C. \( 0.002 s \)
- D. \( 0.324 s \)
Step-by-step solution
Total resistance R = 0.1 Ω + 0.9 Ω = 1.0 Ω, time constant τ = L/R = 0.01 H / 1.0 Ω = 0.01 s. For current to reach 80% of saturation: 1 - e^{-t/τ} = 0.8 → e^{-t/τ} = 0.2 → t/τ = ln 5 = 1.6 → t = 1.6 × 0.01 s = 0.016 s.
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