MHT CET · Physics · Electromagnetic Induction
The magnetic flux through a loop of resistance \(10 \Omega\) varying according to the relation \(\phi=6 \mathrm{t}^2+7 \mathrm{t}+1\), where \(\phi\) is in milliweber, time is in second at time \(t=1 \mathrm{~s}\) the induced e.m.f. is
- A \(12\ mV\)
- B \(7\ mV\)
- C \(19\ mV\)
- D \(19\ V\)
Answer & Solution
Correct Answer
(C) \(19\ mV\)
Step-by-step Solution
Detailed explanation
Given \(\mathrm{R}=10 \Omega, \phi=6 \mathrm{t}^2+7 \mathrm{t}+1 \mathrm{mWb}, \mathrm{t}=1 \mathrm{~s}\)
From \(\mathrm{e}=\frac{\mathrm{d} \phi}{\mathrm{dt}}\),
\(e=\frac{d}{d t}\left(6 t^2+7 t+1\right)=12 t+7\)
Put \(\mathrm{t}=1\) in the above equation,
\(\therefore \quad \mathrm{e}=19 \mathrm{mV}\)
From \(\mathrm{e}=\frac{\mathrm{d} \phi}{\mathrm{dt}}\),
\(e=\frac{d}{d t}\left(6 t^2+7 t+1\right)=12 t+7\)
Put \(\mathrm{t}=1\) in the above equation,
\(\therefore \quad \mathrm{e}=19 \mathrm{mV}\)
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