Question

A triangular wire frame (each side of $2$$m$) is placed in a region of time variant magnetic field having $dB/dt=\sqrt{3}T/s$. The magnetic field is perpendicular to the plane of the triangle. The base of the triangle AB has a resistance $1$$\Omega$ while the other two sides have resistance $2$$\Omega$ each. The magnitude of potential difference between the points A and B will be :

• A. $0.2V$
• B. $0.6V$
• C. $0.3V$
• D. $0.5V$

Answer 1

The correct option is B $0.6V$

Area of triangle, $A=\frac{\sqrt{3}}{4}{a}^2$ where $a$=length of each side

$⟹A=\frac{\sqrt{3}}{4}(2{)}^2=\sqrt{3}{m}^2$

Now,flux=$\varphi =BA=\sqrt{3}B$

magnitude of e.m.f=$E=\frac{d\varphi }{dt}=\sqrt{3}\frac{dB}{dt}$

$⟹E=3V$ since $\frac{dB}{dt}=\sqrt{3}T/s$

Now, resistance of circuit, $R=2+2+1=5ohm$

current in loop=$i=\frac{E}{R}=\frac{3}{5}=0.6A$

Potential difference across AB=$V_{AB}=i\times R_{AB}=0.6\times 1=0.6V$

Answer-(B)