A coil of cross-sectional area $10^2 cm^2$ is is placed in the magnetic field, which changes by $4×10^2\, Wb/m^2$ within 5 sec. What will be the current across 5 Ω resistance?

0.16 A

The correct answer is Option 2 → 0.16 A

Cross-Sectional Area, $A=102cm^2=102×10^{-4}m^2=0.0102m^2$

Change in magnetic field, $ΔB=4×10^2Wb/m^2$

Time interval, $t=5s$

Resistance, $R=5Ω$

Calculate change in Magnetic flux $Δ\phi$

Magnetic flux $\phi=B×A$

So, change in magnetic flux,

$Δ\phi=A×ΔB=0.0102×4×10^2=0.0102×400=4.08Wb$

Calculate induced emf (Faraday's law)

$Emf=\frac{Δ\phi}{t}=\frac{4.08}{5}=0.816V$

Calculate current using ohm's law

$I=\frac{Emf}{R}=\frac{0.816}{5}=0.1632A$