Self inductance and mutual inductance — NEET & JEE Questions

Question 1 · difficulty L1 · recall

Self-inductance is the property by which a changing current in a circuit induces emf

• A. only in a distant unrelated circuit
• B. only in a battery
• C. in the same circuit
• D. only in a resistor with constant current

Question 2 · difficulty L1 · understanding

The SI unit of inductance is

• A. tesla
• B. weber per metre only
• C. farad
• D. henry

Question 3 · difficulty L2 · understanding

The current in an inductor is given by $$\mathrm{I}=(3 \mathrm{t}+8)$$ where $$\mathrm{t}$$ is in second. The magnitude of induced emf produced in the inductor is $$12 \mathrm{~mV}$$. The self-inductance of the inductor _________ $$\mathrm{mH}$$.

Question 4 · difficulty L2 · understanding

Two coils have mutual inductance $$0.002 \mathrm{~H}$$. The current changes in the first coil according to the relation $$\mathrm{i}=\mathrm{i}_0 \sin \omega \mathrm{t}$$, where $$\mathrm{i}_0=5 \mathrm{~A}$$ and $$\omega=50 \pi$$ rad/s. The maximum value of emf in the second coil is $$\frac{\pi}{\alpha} \mathrm{~V}$$. The value of $$\alpha$$ is _______.

Question 5 · difficulty L2 · understanding

For the given circuit the current through battery of 6 V just after closing the switch 'S' will be _________ A.

Question 6 · difficulty L2 · understanding

A 10 $$\Omega$$, 20 mH coil carrying constant current is connected to a battery of 20 V through a switch. Now after switch is opened current becomes zero in 100 $$\mu$$s. The average e.m.f. induced in the coil is ____________ V.

Question 7 · difficulty L2 · understanding

The current in a coil of self inductance 2.0 H is increasing according to I = 2 sin(t 2 ) A. The amount of energy spent during the period when current changes from 0 to 2 A is ____________ J.

Question 8 · difficulty L2 · understanding

A 30 cm long solenoid has 10 turns per cm and area of $5 \mathrm{~cm}^2$. The current through the solenoid coil varies from 2 A to 4 A in 3.14 s . The e.m.f. induced in the coil is $\alpha \times 10^{-5} \mathrm{~V}$. The value $\alpha$ is $\_\_\_\_$ .

• A. 60
• B. 12
• C. 120
• D. 34

Question 9 · difficulty L2 · understanding

$$\text { Match the LIST-I with LIST-II }$$ List-I List-II A. Magnetic induction I. <mi mathvariant="normal">M</mi> <mi mathvariant="normal">L</mi> <mrow data-mjx-texclass="ORD"> <mi mathvariant="normal">T</mi> </mrow> <mrow data-mjx-texclass="ORD"> <mo>−</mo> <mn>2</mn> </mrow> <mrow data-mjx-texclass="ORD"> <mtext> </mtext> <mi mathvariant="normal">A</mi> </mrow> <mrow data-mjx-texclass="ORD"> <mo>−</mo> <mn>2</mn> </mrow> <mi mathvariant="normal">M</mi> <mi mathvariant="normal">L</mi> <mrow data-mjx-texclass="ORD"> <mi mathvariant="normal">T</mi> </mrow> <mrow data-mjx-texclass="ORD"> <mo>−</mo> <mn>2</mn> </mrow> <mrow data-mjx-texclass="ORD"> <mtext></mtext> <mi mathvariant="normal">A</mi> </mrow> <mrow data-mjx-texclass="ORD"> <mo>−</mo> <mn>2</mn> </mrow> MLT^(-2)A^(-2) B. Magnetic flux II. <mi mathvariant="normal">M</mi> <mrow data-mjx-texclass="ORD"> <mi mathvariant="normal">L</mi> </mrow> <mn>2</mn> <mrow data-mjx-texclass="ORD"> <mtext> </mtext> <mi mathvariant="normal">T</mi> </mrow> <mrow data-mjx-texclass="ORD"> <mo>−</mo> <mn>2</mn> </mrow> <mrow data-mjx-texclass="ORD"> <mtext> </mtext> <mi mathvariant="normal">A</mi> </mrow> <mrow data-mjx-texclass="ORD"> <mo>−</mo> <mn>2</mn> </mrow> <mi mathvariant="normal">M</mi> <mrow data-mjx-texclass="ORD"> <mi mathvariant="normal">L</mi> </mrow> <mn>2</mn> <mrow data-mjx-texclass="ORD"> <mtext></mtext> <mi mathvariant="normal">T</mi> </mrow> <mrow data-mjx-texclass="ORD"> <mo>−</mo> <mn>2</mn> </mrow> <mrow data-mjx-texclass="ORD"> <mtext></mtext> <mi mathvariant="normal">A</mi> </mrow> <mrow data-mjx-texclass="ORD"> <mo>−</mo> <mn>2</mn> </mrow> ML^(2)T^(-2)A^(-2) C. Magnetic permeability III. <mi mathvariant="normal">M</mi> <mrow data-mjx-texclass="ORD"> <mi mathvariant="normal">L</mi> </mrow> <mn>0</mn> <mrow data-mjx-texclass="ORD"> <mtext> </mtext> <mi mathvariant="normal">T</mi> </mrow> <mrow data-mjx-texclass="ORD"> <mo>−</mo> <mn>2</mn> </mrow> <mrow data-mjx-texclass="ORD"> <mtext> </mtext> <mi mathvariant="normal">A</mi> </mrow> <mrow data-mjx-texclass="ORD"> <mo>−</mo> <mn>1</mn> </mrow> <mi mathvariant="normal">M</mi> <mrow data-mjx-texclass="ORD"> <mi mathvariant="normal">L</mi> </mrow> <mn>0</mn> <mrow data-mjx-texclass="ORD"> <mtext></mtext> <mi mathvariant="normal">T</mi> </mrow> <mrow data-mjx-texclass="ORD"> <mo>−</mo> <mn>2</mn> </mrow> <mrow data-mjx-texclass="ORD"> <mtext></mtext> <mi mathvariant="normal">A</mi> </mrow> <mrow data-mjx-texclass="ORD"> <mo>−</mo> <mn>1</mn> </mrow> ML^(0)T^(-2)A^(-1) D. Self inductance IV. <mi mathvariant="normal">M</mi> <mrow data-mjx-texclass="ORD"> <mi mathvariant="normal">L</mi> </mrow> <mn>2</mn> <mrow data-mjx-texclass="ORD"> <mtext> </mtext> <mi mathvariant="normal">T</mi> </mrow> <mrow data-mjx-texclass="ORD"> <mo>−</mo> <mn>2</mn> </mrow> <mrow data-mjx-texclass="ORD"> <mtext> </mtext> <mi mathvariant="normal">A</mi> </mrow> <mrow data-mjx-texclass="ORD"> <mo>−</mo> <mn>1</mn> </mrow> <mi mathvariant="normal">M</mi> <mrow data-mjx-texclass="ORD"> <mi mathvariant="normal">L</mi> </mrow> <mn>2</mn> <mrow data-mjx-texclass="ORD"> <mtext></mtext> <mi mathvariant="normal">T</mi> </mrow> <mrow data-mjx-texclass="ORD"> <mo>−</mo> <mn>2</mn> </mrow> <mrow data-mjx-texclass="ORD"> <mtext></mtext> <mi mathvariant="normal">A</mi> </mrow> <mrow data-mjx-texclass="ORD"> <mo>−</mo> <mn>1</mn> </mrow> ML^(2)T^(-2)A^(-1) Choose the correct answer from the options given below:

• A. A-III, B-IV, C-II, D-I
• B. A-I, B-III, C-IV, D-II
• C. A-IV, B-III, C-I, D-II
• D. A-III, B-IV, C-I, D-II

Question 10 · difficulty L2 · understanding

Consider I 1 and I 2 are the currents flowing simultaneously in two nearby coils 1 & 2, respectively. If L 1 = self inductance of coil 1, M 12 = mutual inductance of coil 1 with respect to coil 2, then the value of induced emf in coil 1 will be :

• A. e 1 = -L 1 $\frac{dI_2}{dt}$ - M 12 $\frac{dI_1}{dt}$
• B. e 1 = -L 1 $\frac{dI_1}{dt}$ + M 12 $\frac{dI_2}{dt}$
• C. e 1 = -L 1 $\frac{dI_1}{dt}$ - M 12 $\frac{dI_1}{dt}$
• D. e 1 = -L 1 $\frac{dI_1}{dt}$ - M 12 $\frac{dI_2}{dt}$