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Question

A flat coil of 500 turns each of area 50cm2 rotates in a uniform magnetic field of 0.14Wb/m2 about an axis normal to the field at an angular speed of 150rad/s. The coil has a resistance of 5Ω. the induced e.m.f. is applied to an external resistance of 10Ω, the peak current through the resistance is:


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Solution

Step 1: Given data

Number of turns(N)=500;

Area A=50cm2

B=0.14Wbm-2

ω=150rads-1

R=5Ω

R'=10Ω

Step 2: Formula used

i0=E0R[wherei0=peakcurrent,E0=inducedemf,R=resistance]E0=NBA[whereE0=inducedemf,N=numberofturns,B-magneticflux,A=area]Rtotal=R+R'[R=resistance]

Step 3: Calculating induced emf

The values given are, N=500,A=50cm2=50×10-4m2,B=0.14Wb/m2,ω=150rad/s

Substitute it in the induced emf formula

E0=NBAE0=500×50×10-4×0.14×150E0=52.5V

Step 4: Calculating total resistance

Rtotal=R+R'Rtotal=5Ω+10ΩRtotal=15Ω

Step 4: Calculating peak current

i0=E0Ri0=52.515i0=3.5A

Hence, the value of peak current through the resistance is 3.5A.


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