03. Inductance (Self and Mutual Induction)
Electro Magnetic Induction

154799 A rectangular wire loop with length a and width $b$ lies in the xy-plane as shown. Within the loop, there is a time dependent magnetic field given by $\mathbf{B}=c[(x \cos \omega t) \hat{i}+(y \sin \omega t) \hat{k}]$
Here, $c$ and $\omega$ are constants. The magnitude of emf induced in the loop as a function of time is

1 $\left|\frac{a b^{2} c}{2} \omega \cos \omega t\right|$
2 $\left|a b^{2} \operatorname{coc} \cos \omega t\right|$
3 $\left|\frac{a^{2} b c}{2} \omega \sin \omega t\right|$
4 None of these
Electro Magnetic Induction

154800 Two circular loops $L_{1}$ and $L_{2}$ of wire carrying equal and opposite currents are placed parallel to each other with a common axis. The radius of loop $L_{1}$ is $R_{1}$ and that of $L_{2}$ is $R_{2}$. The distance between the centres of the loops is $\sqrt{3} R_{1}$. The magnetic field at the centre of $L_{2}$ shall be zero, if

1 $\mathrm{R}_{2}=4 \mathrm{R}_{1}$
2 $\mathrm{R}_{2}=2 \mathrm{R}_{1}$
3 $R_{2}=\sqrt{2} R_{1}$
4 $\mathrm{R}_{2}=8 \mathrm{R}_{1}$
Electro Magnetic Induction

154801 A solenoid of radius $R$ has $n$ turns per unit length, then the self-inductance of the solenoid per unit length is

1 $\mu_{0} \mathrm{n} \pi \mathrm{R}^{2}$
2 $\mu_{0} \mathrm{nR}^{2}$
3 $\mu_{0} \mathrm{n}^{2} \mathrm{R}^{2}$
4 $\mu_{0} n^{2} \pi R^{2}$
Electro Magnetic Induction

154802 At $600 \mathrm{~Hz}$, an inductor and capacitor have equal reactances, the ratio of the capacitive reactance to the inductive reactance at $60 \mathrm{~Hz}$ will be

1 $100: 1$
2 $200: 1$
3 $300: 1$
4 $400: 1$
Electro Magnetic Induction

154803 A current of $4 \mathrm{~A}$ flows in a coil when connected to a $12 \mathrm{~V}$ d.c. source. If the same coil is connected to a $12 \mathrm{~V},\left(\frac{25}{\pi}\right) \mathrm{Hz}$ a.c source, a current of $2.4 \mathrm{~A}$ flows in the circuit. The inductance of the coil is

1 $100 \mathrm{mH}$
2 $80 \mathrm{mH}$
3 $60 \mathrm{mH}$
4 $50 \mathrm{mH}$
Electro Magnetic Induction

154799 A rectangular wire loop with length a and width $b$ lies in the xy-plane as shown. Within the loop, there is a time dependent magnetic field given by $\mathbf{B}=c[(x \cos \omega t) \hat{i}+(y \sin \omega t) \hat{k}]$
Here, $c$ and $\omega$ are constants. The magnitude of emf induced in the loop as a function of time is

1 $\left|\frac{a b^{2} c}{2} \omega \cos \omega t\right|$
2 $\left|a b^{2} \operatorname{coc} \cos \omega t\right|$
3 $\left|\frac{a^{2} b c}{2} \omega \sin \omega t\right|$
4 None of these
Electro Magnetic Induction

154800 Two circular loops $L_{1}$ and $L_{2}$ of wire carrying equal and opposite currents are placed parallel to each other with a common axis. The radius of loop $L_{1}$ is $R_{1}$ and that of $L_{2}$ is $R_{2}$. The distance between the centres of the loops is $\sqrt{3} R_{1}$. The magnetic field at the centre of $L_{2}$ shall be zero, if

1 $\mathrm{R}_{2}=4 \mathrm{R}_{1}$
2 $\mathrm{R}_{2}=2 \mathrm{R}_{1}$
3 $R_{2}=\sqrt{2} R_{1}$
4 $\mathrm{R}_{2}=8 \mathrm{R}_{1}$
Electro Magnetic Induction

154801 A solenoid of radius $R$ has $n$ turns per unit length, then the self-inductance of the solenoid per unit length is

1 $\mu_{0} \mathrm{n} \pi \mathrm{R}^{2}$
2 $\mu_{0} \mathrm{nR}^{2}$
3 $\mu_{0} \mathrm{n}^{2} \mathrm{R}^{2}$
4 $\mu_{0} n^{2} \pi R^{2}$
Electro Magnetic Induction

154802 At $600 \mathrm{~Hz}$, an inductor and capacitor have equal reactances, the ratio of the capacitive reactance to the inductive reactance at $60 \mathrm{~Hz}$ will be

1 $100: 1$
2 $200: 1$
3 $300: 1$
4 $400: 1$
Electro Magnetic Induction

154803 A current of $4 \mathrm{~A}$ flows in a coil when connected to a $12 \mathrm{~V}$ d.c. source. If the same coil is connected to a $12 \mathrm{~V},\left(\frac{25}{\pi}\right) \mathrm{Hz}$ a.c source, a current of $2.4 \mathrm{~A}$ flows in the circuit. The inductance of the coil is

1 $100 \mathrm{mH}$
2 $80 \mathrm{mH}$
3 $60 \mathrm{mH}$
4 $50 \mathrm{mH}$
Electro Magnetic Induction

154799 A rectangular wire loop with length a and width $b$ lies in the xy-plane as shown. Within the loop, there is a time dependent magnetic field given by $\mathbf{B}=c[(x \cos \omega t) \hat{i}+(y \sin \omega t) \hat{k}]$
Here, $c$ and $\omega$ are constants. The magnitude of emf induced in the loop as a function of time is

1 $\left|\frac{a b^{2} c}{2} \omega \cos \omega t\right|$
2 $\left|a b^{2} \operatorname{coc} \cos \omega t\right|$
3 $\left|\frac{a^{2} b c}{2} \omega \sin \omega t\right|$
4 None of these
Electro Magnetic Induction

154800 Two circular loops $L_{1}$ and $L_{2}$ of wire carrying equal and opposite currents are placed parallel to each other with a common axis. The radius of loop $L_{1}$ is $R_{1}$ and that of $L_{2}$ is $R_{2}$. The distance between the centres of the loops is $\sqrt{3} R_{1}$. The magnetic field at the centre of $L_{2}$ shall be zero, if

1 $\mathrm{R}_{2}=4 \mathrm{R}_{1}$
2 $\mathrm{R}_{2}=2 \mathrm{R}_{1}$
3 $R_{2}=\sqrt{2} R_{1}$
4 $\mathrm{R}_{2}=8 \mathrm{R}_{1}$
Electro Magnetic Induction

154801 A solenoid of radius $R$ has $n$ turns per unit length, then the self-inductance of the solenoid per unit length is

1 $\mu_{0} \mathrm{n} \pi \mathrm{R}^{2}$
2 $\mu_{0} \mathrm{nR}^{2}$
3 $\mu_{0} \mathrm{n}^{2} \mathrm{R}^{2}$
4 $\mu_{0} n^{2} \pi R^{2}$
Electro Magnetic Induction

154802 At $600 \mathrm{~Hz}$, an inductor and capacitor have equal reactances, the ratio of the capacitive reactance to the inductive reactance at $60 \mathrm{~Hz}$ will be

1 $100: 1$
2 $200: 1$
3 $300: 1$
4 $400: 1$
Electro Magnetic Induction

154803 A current of $4 \mathrm{~A}$ flows in a coil when connected to a $12 \mathrm{~V}$ d.c. source. If the same coil is connected to a $12 \mathrm{~V},\left(\frac{25}{\pi}\right) \mathrm{Hz}$ a.c source, a current of $2.4 \mathrm{~A}$ flows in the circuit. The inductance of the coil is

1 $100 \mathrm{mH}$
2 $80 \mathrm{mH}$
3 $60 \mathrm{mH}$
4 $50 \mathrm{mH}$
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Electro Magnetic Induction

154799 A rectangular wire loop with length a and width $b$ lies in the xy-plane as shown. Within the loop, there is a time dependent magnetic field given by $\mathbf{B}=c[(x \cos \omega t) \hat{i}+(y \sin \omega t) \hat{k}]$
Here, $c$ and $\omega$ are constants. The magnitude of emf induced in the loop as a function of time is

1 $\left|\frac{a b^{2} c}{2} \omega \cos \omega t\right|$
2 $\left|a b^{2} \operatorname{coc} \cos \omega t\right|$
3 $\left|\frac{a^{2} b c}{2} \omega \sin \omega t\right|$
4 None of these
Electro Magnetic Induction

154800 Two circular loops $L_{1}$ and $L_{2}$ of wire carrying equal and opposite currents are placed parallel to each other with a common axis. The radius of loop $L_{1}$ is $R_{1}$ and that of $L_{2}$ is $R_{2}$. The distance between the centres of the loops is $\sqrt{3} R_{1}$. The magnetic field at the centre of $L_{2}$ shall be zero, if

1 $\mathrm{R}_{2}=4 \mathrm{R}_{1}$
2 $\mathrm{R}_{2}=2 \mathrm{R}_{1}$
3 $R_{2}=\sqrt{2} R_{1}$
4 $\mathrm{R}_{2}=8 \mathrm{R}_{1}$
Electro Magnetic Induction

154801 A solenoid of radius $R$ has $n$ turns per unit length, then the self-inductance of the solenoid per unit length is

1 $\mu_{0} \mathrm{n} \pi \mathrm{R}^{2}$
2 $\mu_{0} \mathrm{nR}^{2}$
3 $\mu_{0} \mathrm{n}^{2} \mathrm{R}^{2}$
4 $\mu_{0} n^{2} \pi R^{2}$
Electro Magnetic Induction

154802 At $600 \mathrm{~Hz}$, an inductor and capacitor have equal reactances, the ratio of the capacitive reactance to the inductive reactance at $60 \mathrm{~Hz}$ will be

1 $100: 1$
2 $200: 1$
3 $300: 1$
4 $400: 1$
Electro Magnetic Induction

154803 A current of $4 \mathrm{~A}$ flows in a coil when connected to a $12 \mathrm{~V}$ d.c. source. If the same coil is connected to a $12 \mathrm{~V},\left(\frac{25}{\pi}\right) \mathrm{Hz}$ a.c source, a current of $2.4 \mathrm{~A}$ flows in the circuit. The inductance of the coil is

1 $100 \mathrm{mH}$
2 $80 \mathrm{mH}$
3 $60 \mathrm{mH}$
4 $50 \mathrm{mH}$
Electro Magnetic Induction

154799 A rectangular wire loop with length a and width $b$ lies in the xy-plane as shown. Within the loop, there is a time dependent magnetic field given by $\mathbf{B}=c[(x \cos \omega t) \hat{i}+(y \sin \omega t) \hat{k}]$
Here, $c$ and $\omega$ are constants. The magnitude of emf induced in the loop as a function of time is

1 $\left|\frac{a b^{2} c}{2} \omega \cos \omega t\right|$
2 $\left|a b^{2} \operatorname{coc} \cos \omega t\right|$
3 $\left|\frac{a^{2} b c}{2} \omega \sin \omega t\right|$
4 None of these
Electro Magnetic Induction

154800 Two circular loops $L_{1}$ and $L_{2}$ of wire carrying equal and opposite currents are placed parallel to each other with a common axis. The radius of loop $L_{1}$ is $R_{1}$ and that of $L_{2}$ is $R_{2}$. The distance between the centres of the loops is $\sqrt{3} R_{1}$. The magnetic field at the centre of $L_{2}$ shall be zero, if

1 $\mathrm{R}_{2}=4 \mathrm{R}_{1}$
2 $\mathrm{R}_{2}=2 \mathrm{R}_{1}$
3 $R_{2}=\sqrt{2} R_{1}$
4 $\mathrm{R}_{2}=8 \mathrm{R}_{1}$
Electro Magnetic Induction

154801 A solenoid of radius $R$ has $n$ turns per unit length, then the self-inductance of the solenoid per unit length is

1 $\mu_{0} \mathrm{n} \pi \mathrm{R}^{2}$
2 $\mu_{0} \mathrm{nR}^{2}$
3 $\mu_{0} \mathrm{n}^{2} \mathrm{R}^{2}$
4 $\mu_{0} n^{2} \pi R^{2}$
Electro Magnetic Induction

154802 At $600 \mathrm{~Hz}$, an inductor and capacitor have equal reactances, the ratio of the capacitive reactance to the inductive reactance at $60 \mathrm{~Hz}$ will be

1 $100: 1$
2 $200: 1$
3 $300: 1$
4 $400: 1$
Electro Magnetic Induction

154803 A current of $4 \mathrm{~A}$ flows in a coil when connected to a $12 \mathrm{~V}$ d.c. source. If the same coil is connected to a $12 \mathrm{~V},\left(\frac{25}{\pi}\right) \mathrm{Hz}$ a.c source, a current of $2.4 \mathrm{~A}$ flows in the circuit. The inductance of the coil is

1 $100 \mathrm{mH}$
2 $80 \mathrm{mH}$
3 $60 \mathrm{mH}$
4 $50 \mathrm{mH}$