JEE Mains · Physics · STD 12 -6. Electromagnetic induction
A coil of inductance \(1\,H\) and resistance \(100\,\Omega\) is connected to a battery of \(6\,V\). Determine approximately : \((a)\) The time elapsed before the current acquires half of its steady - state value \((b)\) The energy stored in the magnetic field associated with the coil at an instant \(15\,ms\) after the circuit is switched on. (Given In \(2=0.693\), \(\left.e ^{-3 / 2}=0.25\right)\)
- A \(t =10\,ms ; U =2\,mJ\)
- B \(t =10\,ms ; U =1\,mJ\)
- C \(t =7\,ms ; U =1\,mJ\)
- D \(t =7\,ms ; U =2\,mJ\)
Answer & Solution
Correct Answer
(C) \(t =7\,ms ; U =1\,mJ\)
Step-by-step Solution
Detailed explanation
\(i =\frac{ E }{ R }\left(1- e ^{- t / \tau}\right)\) \(i =\frac{ E }{2 R }=\frac{ E }{ R }\left(1- e ^{- t / \tau)}\right)\) Solving \(t =\tau \ln 2\) \(t =\frac{1}{ R } \ln 2=\frac{1}{100} 0.693=0.00693\) \(=7\,ms\)…
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