A triangular wire frame (each side = 2m) is placed in a region of… - Vidyadip

MCQ

$A$ triangular wire frame (each side $= 2m$) 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....$V$

✓
$0.4$
B
$0.6$
C
$1.2$
D
None

✓

Answer

Correct option: A.

$0.4$

a
$e=\frac{d \phi}{d t}=A \frac{d A}{d t}=\frac{1}{2} 2 \times 2 \sin 60^{\circ} \sqrt{3}=3 V$

Induced emf in each side $=e / 3$

$1 V$

$I=\frac{e}{R}=\frac{3}{1+2+2}=\frac{3}{5} A$

$V_{A}+1-I \times 1=V_{B}$

$\Rightarrow V_{A}-V_{B}=I-1=\frac{-2}{5}$

$=-0.4 V$

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