Problem 4: A coil of resistance 100 Ω is placed in a magnetic field of 1 mWb. The coil has 100 turns and a galvanometer of 400 Ω resistance is connected in series with it: find the average emf and the current if the coil is moved in 1/10^{th} s from the given field to a field of 0.2 mWb.

Solution

Given data No of turns in the coil = 100

Resistance of the coil = R_{1} = 100 Ω Resistance of galvanometer = R_{2} = 400 Ω

Initial magnetic field,B_{1} = 1 mWb Final magnetic field, B_{2} = 0.2 mWb Time for change in the field = 1/10 = 0.1 sec

Required Average emf =? Current, I =?

Formulae

Theory The coil and the galvanometer are connected in series, therefore, the resistance of the circuit is the sum of the resistances of the coil and the galvanometer.

Therefore, resistance of the circuit = 100 + 400 = 500 Ω.

Now change in flux = 1 – 0.2 = 0.8 mWb = 0.8 × 10^{-3} Wb

Apply first formula to find the induced emf.

Apply second formula to find the current in the coil.

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