A coil of n turns and resistance R is connected in series with resistance R / 4 . The combination is moved for time t second through magnetic flux ₁ to ₂ . The induced current in the circuit is

Step-by-step solution

The total circuit resistance combines the coil resistance R with the series resistor of R/4 : R_ total = R + R 4 = 5R 4 By Faraday's law, the magnitude of induced EMF is E = n t = n ( ₁ - ₂) t , as the flux decreases from ₁ to ₂ . Applying Ohm’s law yields the current: I = E R_ total = n ( ₁ - ₂) t 4 5R = 4n ( ₁ - ₂) 5Rt The resulting expression corresponds to option B.