Mutual Inductance — MH-CET Physics MCQs with Solutions
Free MH-CET Physics Mutual Inductance MCQs with step-by-step solutions (21 questions). Part of Electromagnetic Induction. Practise online on Prepizo — no login needed.
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Questions with solutions
Q1 — Mutual Inductance · easy · theory
The mutual inductance between two coils is defined by:
A. $M = \dfrac{\Phi_2}{N_2I_1}$
B. $M = \dfrac{I_1}{N_2\Phi_2}$
C. $M = N_2\Phi_2I_1$
D. $M = \dfrac{N_2\Phi_2}{I_1}$ ✓ Correct
Solution: It is the flux linkage in the secondary per unit current in the primary, measured in henry.
Q2 — Mutual Inductance · easy · theory
The EMF induced in a secondary coil due to a changing current in the primary is:
A. $-\dfrac{M}{I_1}$
B. $-MI_1$
C. $-M\dfrac{dI_1}{dt}$ ✓ Correct
D. $-\dfrac{dI_1}{Mdt}$
Solution: This is the principle on which the transformer and the induction coil work.
Q3 — Mutual Inductance · medium · theory
The mutual inductance of two coaxial solenoids of turn numbers $N_1$ and $N_2$ is proportional to:
A. $\sqrt{N_1N_2}$
B. $N_1 + N_2$
C. $\dfrac{N_1}{N_2}$
D. $N_1N_2$ ✓ Correct
Solution: $M = \dfrac{\mu_0N_1N_2A}{l}$ — the primary makes flux proportional to $N_1$ and the secondary links it $N_2$ times.
Q4 — Mutual Inductance · medium · theory
The coefficient of coupling between two coils is defined as:
A. $k = \dfrac{\sqrt{L_1L_2}}{M}$
B. $k = M\sqrt{L_1L_2}$
C. $k = \dfrac{M}{L_1 + L_2}$
D. $k = \dfrac{M}{\sqrt{L_1L_2}}$ ✓ Correct
Solution: It measures the fraction of the primary flux that links the secondary.
Q5 — Mutual Inductance · hard · theory
The mutual inductance of a pair of coils satisfies:
A. $M_{12}$ and $M_{21}$ are unrelated
B. $M_{12} > M_{21}$ if coil 1 has more turns
C. $M_{12} = M_{21}$, whatever the geometry ✓ Correct
D. $M_{12} < M_{21}$ if coil 1 has more turns
Solution: This reciprocity theorem holds for any pair of circuits, however unequal.
Q6 — Mutual Inductance · easy · theory
A transformer works on the principle of:
A. Mutual induction ✓ Correct
B. Electrostatic induction
C. Eddy current braking
D. Self induction
Solution: The alternating current in the primary produces a changing flux that induces an EMF in the secondary.
Q7 — Mutual Inductance · medium · theory
The mutual inductance of two coils depends on:
A. Their geometry, separation, relative orientation and the core material ✓ Correct
B. Only the current in the primary
C. Only the resistance of the coils
D. Only the applied voltage
Solution: Turning one coil through $90^\circ$ can reduce $M$ almost to zero without changing either coil.
Q8 — Mutual Inductance · medium · theory
The coefficient of coupling $k$ between two coils:
A. Can take any value above $1$
B. Cannot exceed $1$ ✓ Correct
C. Is always exactly $1$
D. Is always negative
Solution: $k = 1$ means every line of flux from one coil links the other, which is the ideal never quite reached in practice.
Q9 — Mutual Inductance · easy · theory
Winding two coils on a common soft iron core rather than on air causes the mutual inductance to:
A. Decrease greatly
B. Increase greatly ✓ Correct
C. Remain unchanged
D. Become zero
Solution: The core concentrates the flux and guides it through the secondary, raising both $M$ and the coupling coefficient.
Q10 — Mutual Inductance · hard · numerical
The current in a primary coil falls from $10\text{ A}$ to $2\text{ A}$ in $0.05\text{ s}$, inducing $16\text{ V}$ in the secondary. The mutual inductance is:
A. $0.2\text{ H}$
B. $0.4\text{ H}$
C. $0.5\text{ H}$
D. $0.1\text{ H}$ ✓ Correct
Solution: $M = \dfrac{e}{dI/dt} = \dfrac{16}{(10-2)/0.05} = \dfrac{16}{160} = 0.1\text{ H}$.
Q11 — Mutual Inductance · easy · numerical
Two coils have mutual inductance $0.2\text{ H}$. If the primary current changes at $10\text{ A}/\text{s}$, the secondary EMF is:
A. $0.02\text{ V}$
B. $50\text{ V}$
C. $2\text{ V}$ ✓ Correct
D. $20\text{ V}$
Solution: $e = M\dfrac{dI}{dt} = 0.2 \times 10 = 2\text{ V}$.
Q12 — Mutual Inductance · medium · numerical
Two coils of self inductance $4\text{ H}$ and $9\text{ H}$ are perfectly coupled. Their mutual inductance is:
A. $36\text{ H}$
B. $3\text{ H}$
C. $6\text{ H}$ ✓ Correct
D. $13\text{ H}$
Solution: With $k = 1$, $M = \sqrt{L_1L_2} = \sqrt{36} = 6\text{ H}$.
Q13 — Mutual Inductance · hard · numerical
Two coils of self inductance $4\text{ H}$ and $9\text{ H}$ have a coupling coefficient of $0.5$. Their mutual inductance is:
A. $3\text{ H}$ ✓ Correct
B. $18\text{ H}$
C. $6\text{ H}$
D. $1.5\text{ H}$
Solution: $M = k\sqrt{L_1L_2} = 0.5 \times 6 = 3\text{ H}$.
Q14 — Mutual Inductance · medium · numerical
Two coils have mutual inductance $0.5\text{ H}$. The primary current changes by $4\text{ A}$ in $0.1\text{ s}$. The secondary EMF is:
A. $20\text{ V}$ ✓ Correct
B. $2\text{ V}$
C. $40\text{ V}$
D. $0.2\text{ V}$
Solution: $e = 0.5 \times \dfrac{4}{0.1} = 0.5 \times 40 = 20\text{ V}$.
Q15 — Mutual Inductance · hard · numerical
A current of $5\text{ A}$ in a primary links a flux of $0.002\text{ Wb}$ with each of the $100$ turns of a secondary. The mutual inductance is:
A. $0.04\text{ H}$ ✓ Correct
B. $2.5\text{ H}$
C. $0.4\text{ H}$
D. $0.004\text{ H}$
Solution: $M = \dfrac{N_2\Phi_2}{I_1} = \dfrac{100 \times 0.002}{5} = 0.04\text{ H}$.
Q16 — Mutual Inductance · medium · numerical
If the number of turns of both coils of a coupled pair is doubled, the mutual inductance becomes:
A. Four times as large ✓ Correct
B. Unchanged
C. Half as large
D. Twice as large
Solution: $M \propto N_1N_2$, so doubling both multiplies $M$ by four.
Q17 — Mutual Inductance · medium · numerical
Two coils have mutual inductance $0.25\text{ H}$. For a secondary EMF of $10\text{ V}$, the primary current must change at:
A. $2.5\text{ A}/\text{s}$
B. $4\text{ A}/\text{s}$
C. $0.025\text{ A}/\text{s}$
D. $40\text{ A}/\text{s}$ ✓ Correct
Solution: $\dfrac{dI}{dt} = \dfrac{e}{M} = \dfrac{10}{0.25} = 40\text{ A}/\text{s}$.
Q18 — Mutual Inductance · easy · numerical
Two coils have mutual inductance $0.1\text{ H}$. If the primary current changes at $50\text{ A}/\text{s}$, the secondary EMF is:
A. $5\text{ V}$ ✓ Correct
B. $0.5\text{ V}$
C. $50\text{ V}$
D. $500\text{ V}$
Solution: $e = 0.1 \times 50 = 5\text{ V}$.
Q19 — Mutual Inductance · medium · numerical
Two identical coils each of self inductance $L$ are perfectly coupled. Their mutual inductance is:
A. $2L$
B. $L$ ✓ Correct
C. $L^2$
D. $\dfrac{L}{2}$
Solution: $M = k\sqrt{L \times L} = 1 \times L = L$.
Q20 — Mutual Inductance · medium · numerical
A coupling coefficient of $k = 1$ between two coils indicates that:
A. The coils have equal inductance
B. All the flux of one coil links the other ✓ Correct
C. The coils are perpendicular to each other
D. No flux of one coil links the other
Solution: Perfect coupling is approached in a well-designed transformer with a closed iron core.
Q21 — Mutual Inductance · hard · numerical
Two coils of self inductance $2\text{ H}$ and $8\text{ H}$ have a mutual inductance of $2\text{ H}$. Their coefficient of coupling is:
A. $1.0$
B. $0.25$
C. $0.5$ ✓ Correct
D. $0.125$
Solution: $k = \dfrac{M}{\sqrt{L_1L_2}} = \dfrac{2}{\sqrt{16}} = \dfrac{2}{4} = 0.5$.