Two identical conducting wires A and B of same dimensions and sam… - Vidyadip

MCQ

Two identical conducting wires $A$ and $B$ of same dimensions and same material are bent in the form of circular coil. Wire $A$ consists of single turn whereas wire $B$ consists of $2\, turns$. Both these wires are then suspended in a uniform magnetic field with their planes parallel to the one another and same current is passed through them. Which statement is correct ?

A
Couple on loop $A$ is more than on loop $B$
B
Couple on loop $B$ is more than on loop $A$
C
Couples on both the loop are equal
D
Couple on loop $B$ is twice that on loop $A$

✓

Answer

$\mathrm{C}=\mathrm{NiAB} \sin \theta$

$\mathrm{C} \propto \mathrm{N} \cdot \mathrm{A}$

Here $\quad \frac{\mathrm{N}_{\mathrm{A}}}{\mathrm{N}_{\mathrm{B}}}=\frac{1}{2}$

If $\mathrm{r}_{\mathrm{A}}$ and $\mathrm{r}_{\mathrm{B}}$ be the radii of the circular loops $\mathrm{A}$ and $\mathrm{B}$ respectively, then the length $\ell$ of both the wires,

${\ell=2 \pi \mathrm{r}_{\mathrm{A}}=2 \times 2 \pi \mathrm{r}_{\mathrm{B}}}$

${\mathrm{r}_{\mathrm{A}}=2 \mathrm{r}_{\mathrm{B}}}$

Their cross-sectional areas $\mathrm{A}_{\mathrm{A}}$ and $\mathrm{A}_{\mathrm{B}}$ are in the ratio

$\frac{\mathrm{A}_{\mathrm{A}}}{\mathrm{A}_{\mathrm{B}}}=\frac{\pi \mathrm{r}_{\mathrm{A}}^{2}}{\pi \mathrm{r}_{\mathrm{B}}^{2}}=4$

Now, the ratio of couples on the two coils is

${\frac{C_{A}}{C_{B}}=\frac{N_{A}}{N_{B}} \frac{A_{A}}{A_{B}}=\frac{1}{2} \times 4=2} $

${C_{A}=2 C_{B}}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from Magnetic Effect of Current→Magnetic Effect of Current — all question types→JEE physics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

Oxygen is $16$ times heavier than hydrogen. Equal volumes of hydrogen and oxygen are mixed. The ratio of speed of sound in the mixture to that in hydrogen is

The maximum force, in addition to the weight required to pull a wire of $5.0 \mathrm{~cm}$ long from the surface of water at temperature $20\ \mathrm{C}$, is $728$ dynes. The surface tension of water is

Which is not true with respect to the cathode rays

The volume of a gas is reduced adiabatically to $\frac{1}{4}$ of its volume at $27^{\circ} \mathrm{C}$, if the value of $\gamma=1.4$, then the new temperature will be

The electron in a hydrogen atom makes a transition from an excited state to the ground state. Which of the following statements is true

The conductivity of a superconductor is

Two coherent sources of different intensities send waves which interfere. The ratio of maximum intensity to the minimum intensity is $25.$ The intensities of the sources are in the ratio

In an astronomical telescope, the focal length of the objective lens is $100 \mathrm{~cm}$ and of eye-piece is $2 \mathrm{~cm}$. The magnifying power of the telescope for the normal eye is

In a circuit containing an inductance of zero resistance, the e.m.f. of the applied ac voltage leads the current by

A Carnot's engine is made to work between $200^{\circ} \mathrm{C}$ and $0^{\circ} \mathrm{C}$ first and then between $0^{\circ} \mathrm{C}$ and $-200^{\circ} \mathrm{C}$. The ratio of efficiencies of the engine in the two cases is