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CBSE Class 12-science Answered

A coil is needed to operate an arc lamp of 150 V, 50 Hz. The lamp of resistance of 5 ohms when running at 10A. Find inductance of the choke coil, if the same arc lamp is to be operated on 160 V, DC. What is the additional resistance required? Compare the power losses in each case.
Asked by lekhakarthikeyan | 29 Jul, 2018, 04:16: PM
answered-by-expert Expert Answer
current in LR circuit begin mathsize 12px style equals space V over z space equals space fraction numerator V over denominator square root of R squared plus left parenthesis omega L right parenthesis squared end root end fraction space equals space fraction numerator 150 over denominator square root of 25 plus 4 pi squared cross times 50 cross times 50 cross times L squared end root end fraction space equals space 10 end style A ................(1)

V - voltage, z is impedence, R is resistance, ω(=2πf) is angular frequency anfd f = 50 Hz. L is inductance
 
Solving eqn.(1) for L , we get L = 0.045 Henry
 
when voltage is 160V, we calculate the resistance with the same formula by substituting L = 0.045 Henry.
In that case we get R = 7.5Ω. since the lamp resistance is 5Ω, we need to add 2.5Ω addiitinal resistance in the circuit
Answered by Thiyagarajan K | 31 Jul, 2018, 11:52: AM
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