358511
If the current \(30\;A\) flowing in the primary coil is made zero in \(0.1\sec .\) The emf induced in the secondary coil is 1.5 volt. The mutual inductance between the coils is:
358512
A small square loop of wire of side \(l\) is placed inside a large square loops of wire of side \(L(L > l)\). The loops are coplanar and their centres coincide. The mutual inductance of the system is proportional to:
1 \(l/L\)
2 \(l^{2} / L\)
3 \(L / l\)
4 \(L^{2} / l\)
Explanation:
Magnetic field produced due to large loop at its centre is \(B=\dfrac{\mu_{0}}{4 \pi} \dfrac{8 \sqrt{2 i}}{L}\)
Flux linked with smaller loop \(\begin{aligned}& \phi=B(l)^{2}=\dfrac{\mu_{0}}{4 \pi} \dfrac{8 \pi i l^{2}}{L} \\& \phi=M i \Rightarrow M=\dfrac{\phi}{i}=\dfrac{\mu_{0}}{4 \pi} \cdot \dfrac{8 \sqrt{2} l^{2}}{L} \\& \Rightarrow M \alpha \dfrac{l^{2}}{L}\end{aligned}\)
PHXII06:ELECTROMAGNETIC INDUCTION
358513
Find the mutual inductance between two rectangular loops, shown in the figure
Let \(i\) be the current flowing in the large rectangle. Consider a small rectangle of width \(dx\) as shown in the figure.
The flux through the strip is \(\begin{aligned}& d \phi=\dfrac{\mu_{o} i}{2 \pi}\left[\dfrac{1}{x}-\dfrac{1}{x+a}\right] b d x \\& \phi=\dfrac{\mu_{o} i b}{2 \pi} \int_{c}^{c+b}\left[\dfrac{1}{x} d x-\dfrac{1}{x+a} d x\right] \\& \phi=\dfrac{\mu_{o} i b}{2 \pi}\left[\ln \left(\dfrac{c+b}{c}\right)-\ln \left(\dfrac{a+b+c}{a+c}\right)\right]=M i \\& M=\dfrac{\mu_{o} b}{2 \pi}\left[\ln \left(\dfrac{c+b}{c}\right)-\ln \left(\dfrac{a+b+c}{a+c}\right)\right]\end{aligned}\)
PHXII06:ELECTROMAGNETIC INDUCTION
358514
Statement A : Mutual inductance of a pair of coils depend on their separation as well as their relative orientation. Statement B : Mutual inductance depends upon the length of the coils.
1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both statements are correct.
4 Both Statements are incorrect.
Explanation:
Conceptual Question
PHXII06:ELECTROMAGNETIC INDUCTION
358515
Assertion : When two coils are wound on each other the mutual induction between the coils is maximum. Reason : Mutual induction does not depend on the orientation of the coils.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
The assertion is accurate when it describes that when two coils are wound closely on each other, maximum flux linkage occurs and so it maximizes mutual induction between them. But, the reason is false. The orientation of the coils does impact mutual induction to some extent. So correct option is (3).
358511
If the current \(30\;A\) flowing in the primary coil is made zero in \(0.1\sec .\) The emf induced in the secondary coil is 1.5 volt. The mutual inductance between the coils is:
358512
A small square loop of wire of side \(l\) is placed inside a large square loops of wire of side \(L(L > l)\). The loops are coplanar and their centres coincide. The mutual inductance of the system is proportional to:
1 \(l/L\)
2 \(l^{2} / L\)
3 \(L / l\)
4 \(L^{2} / l\)
Explanation:
Magnetic field produced due to large loop at its centre is \(B=\dfrac{\mu_{0}}{4 \pi} \dfrac{8 \sqrt{2 i}}{L}\)
Flux linked with smaller loop \(\begin{aligned}& \phi=B(l)^{2}=\dfrac{\mu_{0}}{4 \pi} \dfrac{8 \pi i l^{2}}{L} \\& \phi=M i \Rightarrow M=\dfrac{\phi}{i}=\dfrac{\mu_{0}}{4 \pi} \cdot \dfrac{8 \sqrt{2} l^{2}}{L} \\& \Rightarrow M \alpha \dfrac{l^{2}}{L}\end{aligned}\)
PHXII06:ELECTROMAGNETIC INDUCTION
358513
Find the mutual inductance between two rectangular loops, shown in the figure
Let \(i\) be the current flowing in the large rectangle. Consider a small rectangle of width \(dx\) as shown in the figure.
The flux through the strip is \(\begin{aligned}& d \phi=\dfrac{\mu_{o} i}{2 \pi}\left[\dfrac{1}{x}-\dfrac{1}{x+a}\right] b d x \\& \phi=\dfrac{\mu_{o} i b}{2 \pi} \int_{c}^{c+b}\left[\dfrac{1}{x} d x-\dfrac{1}{x+a} d x\right] \\& \phi=\dfrac{\mu_{o} i b}{2 \pi}\left[\ln \left(\dfrac{c+b}{c}\right)-\ln \left(\dfrac{a+b+c}{a+c}\right)\right]=M i \\& M=\dfrac{\mu_{o} b}{2 \pi}\left[\ln \left(\dfrac{c+b}{c}\right)-\ln \left(\dfrac{a+b+c}{a+c}\right)\right]\end{aligned}\)
PHXII06:ELECTROMAGNETIC INDUCTION
358514
Statement A : Mutual inductance of a pair of coils depend on their separation as well as their relative orientation. Statement B : Mutual inductance depends upon the length of the coils.
1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both statements are correct.
4 Both Statements are incorrect.
Explanation:
Conceptual Question
PHXII06:ELECTROMAGNETIC INDUCTION
358515
Assertion : When two coils are wound on each other the mutual induction between the coils is maximum. Reason : Mutual induction does not depend on the orientation of the coils.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
The assertion is accurate when it describes that when two coils are wound closely on each other, maximum flux linkage occurs and so it maximizes mutual induction between them. But, the reason is false. The orientation of the coils does impact mutual induction to some extent. So correct option is (3).
358511
If the current \(30\;A\) flowing in the primary coil is made zero in \(0.1\sec .\) The emf induced in the secondary coil is 1.5 volt. The mutual inductance between the coils is:
358512
A small square loop of wire of side \(l\) is placed inside a large square loops of wire of side \(L(L > l)\). The loops are coplanar and their centres coincide. The mutual inductance of the system is proportional to:
1 \(l/L\)
2 \(l^{2} / L\)
3 \(L / l\)
4 \(L^{2} / l\)
Explanation:
Magnetic field produced due to large loop at its centre is \(B=\dfrac{\mu_{0}}{4 \pi} \dfrac{8 \sqrt{2 i}}{L}\)
Flux linked with smaller loop \(\begin{aligned}& \phi=B(l)^{2}=\dfrac{\mu_{0}}{4 \pi} \dfrac{8 \pi i l^{2}}{L} \\& \phi=M i \Rightarrow M=\dfrac{\phi}{i}=\dfrac{\mu_{0}}{4 \pi} \cdot \dfrac{8 \sqrt{2} l^{2}}{L} \\& \Rightarrow M \alpha \dfrac{l^{2}}{L}\end{aligned}\)
PHXII06:ELECTROMAGNETIC INDUCTION
358513
Find the mutual inductance between two rectangular loops, shown in the figure
Let \(i\) be the current flowing in the large rectangle. Consider a small rectangle of width \(dx\) as shown in the figure.
The flux through the strip is \(\begin{aligned}& d \phi=\dfrac{\mu_{o} i}{2 \pi}\left[\dfrac{1}{x}-\dfrac{1}{x+a}\right] b d x \\& \phi=\dfrac{\mu_{o} i b}{2 \pi} \int_{c}^{c+b}\left[\dfrac{1}{x} d x-\dfrac{1}{x+a} d x\right] \\& \phi=\dfrac{\mu_{o} i b}{2 \pi}\left[\ln \left(\dfrac{c+b}{c}\right)-\ln \left(\dfrac{a+b+c}{a+c}\right)\right]=M i \\& M=\dfrac{\mu_{o} b}{2 \pi}\left[\ln \left(\dfrac{c+b}{c}\right)-\ln \left(\dfrac{a+b+c}{a+c}\right)\right]\end{aligned}\)
PHXII06:ELECTROMAGNETIC INDUCTION
358514
Statement A : Mutual inductance of a pair of coils depend on their separation as well as their relative orientation. Statement B : Mutual inductance depends upon the length of the coils.
1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both statements are correct.
4 Both Statements are incorrect.
Explanation:
Conceptual Question
PHXII06:ELECTROMAGNETIC INDUCTION
358515
Assertion : When two coils are wound on each other the mutual induction between the coils is maximum. Reason : Mutual induction does not depend on the orientation of the coils.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
The assertion is accurate when it describes that when two coils are wound closely on each other, maximum flux linkage occurs and so it maximizes mutual induction between them. But, the reason is false. The orientation of the coils does impact mutual induction to some extent. So correct option is (3).
358511
If the current \(30\;A\) flowing in the primary coil is made zero in \(0.1\sec .\) The emf induced in the secondary coil is 1.5 volt. The mutual inductance between the coils is:
358512
A small square loop of wire of side \(l\) is placed inside a large square loops of wire of side \(L(L > l)\). The loops are coplanar and their centres coincide. The mutual inductance of the system is proportional to:
1 \(l/L\)
2 \(l^{2} / L\)
3 \(L / l\)
4 \(L^{2} / l\)
Explanation:
Magnetic field produced due to large loop at its centre is \(B=\dfrac{\mu_{0}}{4 \pi} \dfrac{8 \sqrt{2 i}}{L}\)
Flux linked with smaller loop \(\begin{aligned}& \phi=B(l)^{2}=\dfrac{\mu_{0}}{4 \pi} \dfrac{8 \pi i l^{2}}{L} \\& \phi=M i \Rightarrow M=\dfrac{\phi}{i}=\dfrac{\mu_{0}}{4 \pi} \cdot \dfrac{8 \sqrt{2} l^{2}}{L} \\& \Rightarrow M \alpha \dfrac{l^{2}}{L}\end{aligned}\)
PHXII06:ELECTROMAGNETIC INDUCTION
358513
Find the mutual inductance between two rectangular loops, shown in the figure
Let \(i\) be the current flowing in the large rectangle. Consider a small rectangle of width \(dx\) as shown in the figure.
The flux through the strip is \(\begin{aligned}& d \phi=\dfrac{\mu_{o} i}{2 \pi}\left[\dfrac{1}{x}-\dfrac{1}{x+a}\right] b d x \\& \phi=\dfrac{\mu_{o} i b}{2 \pi} \int_{c}^{c+b}\left[\dfrac{1}{x} d x-\dfrac{1}{x+a} d x\right] \\& \phi=\dfrac{\mu_{o} i b}{2 \pi}\left[\ln \left(\dfrac{c+b}{c}\right)-\ln \left(\dfrac{a+b+c}{a+c}\right)\right]=M i \\& M=\dfrac{\mu_{o} b}{2 \pi}\left[\ln \left(\dfrac{c+b}{c}\right)-\ln \left(\dfrac{a+b+c}{a+c}\right)\right]\end{aligned}\)
PHXII06:ELECTROMAGNETIC INDUCTION
358514
Statement A : Mutual inductance of a pair of coils depend on their separation as well as their relative orientation. Statement B : Mutual inductance depends upon the length of the coils.
1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both statements are correct.
4 Both Statements are incorrect.
Explanation:
Conceptual Question
PHXII06:ELECTROMAGNETIC INDUCTION
358515
Assertion : When two coils are wound on each other the mutual induction between the coils is maximum. Reason : Mutual induction does not depend on the orientation of the coils.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
The assertion is accurate when it describes that when two coils are wound closely on each other, maximum flux linkage occurs and so it maximizes mutual induction between them. But, the reason is false. The orientation of the coils does impact mutual induction to some extent. So correct option is (3).
358511
If the current \(30\;A\) flowing in the primary coil is made zero in \(0.1\sec .\) The emf induced in the secondary coil is 1.5 volt. The mutual inductance between the coils is:
358512
A small square loop of wire of side \(l\) is placed inside a large square loops of wire of side \(L(L > l)\). The loops are coplanar and their centres coincide. The mutual inductance of the system is proportional to:
1 \(l/L\)
2 \(l^{2} / L\)
3 \(L / l\)
4 \(L^{2} / l\)
Explanation:
Magnetic field produced due to large loop at its centre is \(B=\dfrac{\mu_{0}}{4 \pi} \dfrac{8 \sqrt{2 i}}{L}\)
Flux linked with smaller loop \(\begin{aligned}& \phi=B(l)^{2}=\dfrac{\mu_{0}}{4 \pi} \dfrac{8 \pi i l^{2}}{L} \\& \phi=M i \Rightarrow M=\dfrac{\phi}{i}=\dfrac{\mu_{0}}{4 \pi} \cdot \dfrac{8 \sqrt{2} l^{2}}{L} \\& \Rightarrow M \alpha \dfrac{l^{2}}{L}\end{aligned}\)
PHXII06:ELECTROMAGNETIC INDUCTION
358513
Find the mutual inductance between two rectangular loops, shown in the figure
Let \(i\) be the current flowing in the large rectangle. Consider a small rectangle of width \(dx\) as shown in the figure.
The flux through the strip is \(\begin{aligned}& d \phi=\dfrac{\mu_{o} i}{2 \pi}\left[\dfrac{1}{x}-\dfrac{1}{x+a}\right] b d x \\& \phi=\dfrac{\mu_{o} i b}{2 \pi} \int_{c}^{c+b}\left[\dfrac{1}{x} d x-\dfrac{1}{x+a} d x\right] \\& \phi=\dfrac{\mu_{o} i b}{2 \pi}\left[\ln \left(\dfrac{c+b}{c}\right)-\ln \left(\dfrac{a+b+c}{a+c}\right)\right]=M i \\& M=\dfrac{\mu_{o} b}{2 \pi}\left[\ln \left(\dfrac{c+b}{c}\right)-\ln \left(\dfrac{a+b+c}{a+c}\right)\right]\end{aligned}\)
PHXII06:ELECTROMAGNETIC INDUCTION
358514
Statement A : Mutual inductance of a pair of coils depend on their separation as well as their relative orientation. Statement B : Mutual inductance depends upon the length of the coils.
1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both statements are correct.
4 Both Statements are incorrect.
Explanation:
Conceptual Question
PHXII06:ELECTROMAGNETIC INDUCTION
358515
Assertion : When two coils are wound on each other the mutual induction between the coils is maximum. Reason : Mutual induction does not depend on the orientation of the coils.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
The assertion is accurate when it describes that when two coils are wound closely on each other, maximum flux linkage occurs and so it maximizes mutual induction between them. But, the reason is false. The orientation of the coils does impact mutual induction to some extent. So correct option is (3).
