358516
Two coils have a mutual inductance of \(0.01\,H\). The current in the first coil changes according to equation \(I=5 \sin 200 \pi t\). The maximum value of emf induced in the second coils is
1 \(10\,\pi V\)
2 \(0.1\,\pi V\)
3 \(\pi V\)
4 \(0.01\,\pi V\)
Explanation:
Given, mutual inductance in the coil, \(M = 0.01H\) and current in the first coil, \(I=5 \sin 200 \pi t\) Emf induced in secondary coil is given \(e=M \dfrac{d I}{d t}\) Putting the values in above relation, \(\begin{aligned}& e=0.01 \times \dfrac{d}{d t}(5 \sin 200 \pi t) \\& =0.01 \times 5 \times 200 \pi \cos 200 \pi t=10 \pi \cos 200 \pi t\end{aligned}\) Hence, from the equation of emf, the maximum value of emf induced in the coil is \({e_0} = 10\pi V\)
MHTCET - 2019
PHXII06:ELECTROMAGNETIC INDUCTION
358517
Find the mutual inductance of a straight long wire and a rectangular loop, as shown in the figure
Consider a rectangular strip of width \(dx\) and length \(b\). Let \(i\) be the current through the straight wire
Flux through the strip is \(\begin{gathered}d \phi=\dfrac{\mu_{o} i}{2 \pi x}(b d x) \\\phi=\dfrac{\mu_{o} i b}{2 \pi x} \int_{x_{o}}^{x_{o}+a} \dfrac{1}{x} d x=\dfrac{\mu_{o} i b}{2 \pi} \ln \left(\dfrac{x_{o}+a}{x_{o}}\right)=M i \\M=\dfrac{\mu_{o} b}{2 \pi} \ln \left(\dfrac{x_{o}+a}{x_{o}}\right)\end{gathered}\)
PHXII06:ELECTROMAGNETIC INDUCTION
358518
Two coils of self-inductance \(L_{1}\) and \(L_{2}\) are placed closer to each other so that total flux in one coil is completely linked with other. If \(M\) is mutual inductance between them, then
358519
Two coils \(A\) and \(B\) have mutual inductance \(2 \times 10^{-2}\) Henry. If the current in the primary is \(i = 5\sin 10\pi t\), then the maximum value of emf induced in coil \(B\) is
1 \(\pi\) volt
2 \(\dfrac{\pi}{2}\) volt
3 \(\dfrac{\pi}{3}\) volt
4 \(\dfrac{\pi}{4}\) volt
Explanation:
\(M=2 \times 10^{-2} H \text { and } i=5 \sin 10 \pi t\) Induced emf, \(e_{B}=-M \dfrac{d i_{A}}{d t}\) Where, \(e_{B}=\) emf in coil \(B\) \(\begin{aligned}& e_{B}=-2 \times 10^{-2} \dfrac{d}{d t}[5 \sin 10 \pi t] \\& {[i=5 \sin 10 \pi t]} \\& e_{B}=-2 \times 5 \times 10^{-2} \times 10 \pi[\cos 10 \pi t] \\& e_{B}=-\pi[\cos 10 \pi t]\end{aligned}\) The maximum value of emf induced in coil \(\mathrm{B}=\pi \text { volt }\)
NEET Test Series from KOTA - 10 Papers In MS WORD
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PHXII06:ELECTROMAGNETIC INDUCTION
358516
Two coils have a mutual inductance of \(0.01\,H\). The current in the first coil changes according to equation \(I=5 \sin 200 \pi t\). The maximum value of emf induced in the second coils is
1 \(10\,\pi V\)
2 \(0.1\,\pi V\)
3 \(\pi V\)
4 \(0.01\,\pi V\)
Explanation:
Given, mutual inductance in the coil, \(M = 0.01H\) and current in the first coil, \(I=5 \sin 200 \pi t\) Emf induced in secondary coil is given \(e=M \dfrac{d I}{d t}\) Putting the values in above relation, \(\begin{aligned}& e=0.01 \times \dfrac{d}{d t}(5 \sin 200 \pi t) \\& =0.01 \times 5 \times 200 \pi \cos 200 \pi t=10 \pi \cos 200 \pi t\end{aligned}\) Hence, from the equation of emf, the maximum value of emf induced in the coil is \({e_0} = 10\pi V\)
MHTCET - 2019
PHXII06:ELECTROMAGNETIC INDUCTION
358517
Find the mutual inductance of a straight long wire and a rectangular loop, as shown in the figure
Consider a rectangular strip of width \(dx\) and length \(b\). Let \(i\) be the current through the straight wire
Flux through the strip is \(\begin{gathered}d \phi=\dfrac{\mu_{o} i}{2 \pi x}(b d x) \\\phi=\dfrac{\mu_{o} i b}{2 \pi x} \int_{x_{o}}^{x_{o}+a} \dfrac{1}{x} d x=\dfrac{\mu_{o} i b}{2 \pi} \ln \left(\dfrac{x_{o}+a}{x_{o}}\right)=M i \\M=\dfrac{\mu_{o} b}{2 \pi} \ln \left(\dfrac{x_{o}+a}{x_{o}}\right)\end{gathered}\)
PHXII06:ELECTROMAGNETIC INDUCTION
358518
Two coils of self-inductance \(L_{1}\) and \(L_{2}\) are placed closer to each other so that total flux in one coil is completely linked with other. If \(M\) is mutual inductance between them, then
358519
Two coils \(A\) and \(B\) have mutual inductance \(2 \times 10^{-2}\) Henry. If the current in the primary is \(i = 5\sin 10\pi t\), then the maximum value of emf induced in coil \(B\) is
1 \(\pi\) volt
2 \(\dfrac{\pi}{2}\) volt
3 \(\dfrac{\pi}{3}\) volt
4 \(\dfrac{\pi}{4}\) volt
Explanation:
\(M=2 \times 10^{-2} H \text { and } i=5 \sin 10 \pi t\) Induced emf, \(e_{B}=-M \dfrac{d i_{A}}{d t}\) Where, \(e_{B}=\) emf in coil \(B\) \(\begin{aligned}& e_{B}=-2 \times 10^{-2} \dfrac{d}{d t}[5 \sin 10 \pi t] \\& {[i=5 \sin 10 \pi t]} \\& e_{B}=-2 \times 5 \times 10^{-2} \times 10 \pi[\cos 10 \pi t] \\& e_{B}=-\pi[\cos 10 \pi t]\end{aligned}\) The maximum value of emf induced in coil \(\mathrm{B}=\pi \text { volt }\)
358516
Two coils have a mutual inductance of \(0.01\,H\). The current in the first coil changes according to equation \(I=5 \sin 200 \pi t\). The maximum value of emf induced in the second coils is
1 \(10\,\pi V\)
2 \(0.1\,\pi V\)
3 \(\pi V\)
4 \(0.01\,\pi V\)
Explanation:
Given, mutual inductance in the coil, \(M = 0.01H\) and current in the first coil, \(I=5 \sin 200 \pi t\) Emf induced in secondary coil is given \(e=M \dfrac{d I}{d t}\) Putting the values in above relation, \(\begin{aligned}& e=0.01 \times \dfrac{d}{d t}(5 \sin 200 \pi t) \\& =0.01 \times 5 \times 200 \pi \cos 200 \pi t=10 \pi \cos 200 \pi t\end{aligned}\) Hence, from the equation of emf, the maximum value of emf induced in the coil is \({e_0} = 10\pi V\)
MHTCET - 2019
PHXII06:ELECTROMAGNETIC INDUCTION
358517
Find the mutual inductance of a straight long wire and a rectangular loop, as shown in the figure
Consider a rectangular strip of width \(dx\) and length \(b\). Let \(i\) be the current through the straight wire
Flux through the strip is \(\begin{gathered}d \phi=\dfrac{\mu_{o} i}{2 \pi x}(b d x) \\\phi=\dfrac{\mu_{o} i b}{2 \pi x} \int_{x_{o}}^{x_{o}+a} \dfrac{1}{x} d x=\dfrac{\mu_{o} i b}{2 \pi} \ln \left(\dfrac{x_{o}+a}{x_{o}}\right)=M i \\M=\dfrac{\mu_{o} b}{2 \pi} \ln \left(\dfrac{x_{o}+a}{x_{o}}\right)\end{gathered}\)
PHXII06:ELECTROMAGNETIC INDUCTION
358518
Two coils of self-inductance \(L_{1}\) and \(L_{2}\) are placed closer to each other so that total flux in one coil is completely linked with other. If \(M\) is mutual inductance between them, then
358519
Two coils \(A\) and \(B\) have mutual inductance \(2 \times 10^{-2}\) Henry. If the current in the primary is \(i = 5\sin 10\pi t\), then the maximum value of emf induced in coil \(B\) is
1 \(\pi\) volt
2 \(\dfrac{\pi}{2}\) volt
3 \(\dfrac{\pi}{3}\) volt
4 \(\dfrac{\pi}{4}\) volt
Explanation:
\(M=2 \times 10^{-2} H \text { and } i=5 \sin 10 \pi t\) Induced emf, \(e_{B}=-M \dfrac{d i_{A}}{d t}\) Where, \(e_{B}=\) emf in coil \(B\) \(\begin{aligned}& e_{B}=-2 \times 10^{-2} \dfrac{d}{d t}[5 \sin 10 \pi t] \\& {[i=5 \sin 10 \pi t]} \\& e_{B}=-2 \times 5 \times 10^{-2} \times 10 \pi[\cos 10 \pi t] \\& e_{B}=-\pi[\cos 10 \pi t]\end{aligned}\) The maximum value of emf induced in coil \(\mathrm{B}=\pi \text { volt }\)
358516
Two coils have a mutual inductance of \(0.01\,H\). The current in the first coil changes according to equation \(I=5 \sin 200 \pi t\). The maximum value of emf induced in the second coils is
1 \(10\,\pi V\)
2 \(0.1\,\pi V\)
3 \(\pi V\)
4 \(0.01\,\pi V\)
Explanation:
Given, mutual inductance in the coil, \(M = 0.01H\) and current in the first coil, \(I=5 \sin 200 \pi t\) Emf induced in secondary coil is given \(e=M \dfrac{d I}{d t}\) Putting the values in above relation, \(\begin{aligned}& e=0.01 \times \dfrac{d}{d t}(5 \sin 200 \pi t) \\& =0.01 \times 5 \times 200 \pi \cos 200 \pi t=10 \pi \cos 200 \pi t\end{aligned}\) Hence, from the equation of emf, the maximum value of emf induced in the coil is \({e_0} = 10\pi V\)
MHTCET - 2019
PHXII06:ELECTROMAGNETIC INDUCTION
358517
Find the mutual inductance of a straight long wire and a rectangular loop, as shown in the figure
Consider a rectangular strip of width \(dx\) and length \(b\). Let \(i\) be the current through the straight wire
Flux through the strip is \(\begin{gathered}d \phi=\dfrac{\mu_{o} i}{2 \pi x}(b d x) \\\phi=\dfrac{\mu_{o} i b}{2 \pi x} \int_{x_{o}}^{x_{o}+a} \dfrac{1}{x} d x=\dfrac{\mu_{o} i b}{2 \pi} \ln \left(\dfrac{x_{o}+a}{x_{o}}\right)=M i \\M=\dfrac{\mu_{o} b}{2 \pi} \ln \left(\dfrac{x_{o}+a}{x_{o}}\right)\end{gathered}\)
PHXII06:ELECTROMAGNETIC INDUCTION
358518
Two coils of self-inductance \(L_{1}\) and \(L_{2}\) are placed closer to each other so that total flux in one coil is completely linked with other. If \(M\) is mutual inductance between them, then
358519
Two coils \(A\) and \(B\) have mutual inductance \(2 \times 10^{-2}\) Henry. If the current in the primary is \(i = 5\sin 10\pi t\), then the maximum value of emf induced in coil \(B\) is
1 \(\pi\) volt
2 \(\dfrac{\pi}{2}\) volt
3 \(\dfrac{\pi}{3}\) volt
4 \(\dfrac{\pi}{4}\) volt
Explanation:
\(M=2 \times 10^{-2} H \text { and } i=5 \sin 10 \pi t\) Induced emf, \(e_{B}=-M \dfrac{d i_{A}}{d t}\) Where, \(e_{B}=\) emf in coil \(B\) \(\begin{aligned}& e_{B}=-2 \times 10^{-2} \dfrac{d}{d t}[5 \sin 10 \pi t] \\& {[i=5 \sin 10 \pi t]} \\& e_{B}=-2 \times 5 \times 10^{-2} \times 10 \pi[\cos 10 \pi t] \\& e_{B}=-\pi[\cos 10 \pi t]\end{aligned}\) The maximum value of emf induced in coil \(\mathrm{B}=\pi \text { volt }\)
