MHT CET · Physics · Electromagnetic Induction
A coil of resistance \(250 \Omega\) is placed in a magnetic field. If the magnetic flux ( \(\phi\) ) linked with the coil varies with time t (s) as \(\phi=50 \mathrm{t}^2+7\). The current in the coil at \(t=4 \mathrm{~s}\) is
- A 1.3 A
- B 1.4 A
- C \(1.5 \mathrm{~A}\)
- D \(1.6 \mathrm{~A}\)
Answer & Solution
Correct Answer
(D) \(1.6 \mathrm{~A}\)
Step-by-step Solution
Detailed explanation
Induced e.m.f. is given as \(|e|=\frac{d \phi}{d t}\) Given, \(\phi=50 \mathrm{t}^2+7\)
\(\therefore \quad|e|=\frac{d}{d t}\left(50 t^2+7\right)=100 t\)
For \(\mathrm{t}=4 \mathrm{~s}\), \(e=100(4)=400 \mathrm{~V}\)
Current, \(I=\frac{V}{R}=\frac{400}{250}=1.6 \mathrm{~A}\)
\(\therefore \quad|e|=\frac{d}{d t}\left(50 t^2+7\right)=100 t\)
For \(\mathrm{t}=4 \mathrm{~s}\), \(e=100(4)=400 \mathrm{~V}\)
Current, \(I=\frac{V}{R}=\frac{400}{250}=1.6 \mathrm{~A}\)
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