An electric device, which runs at 80 volt d.c. and consumes 10 A current , is connected to 100 vol-50 Hz a.c. supply through a choke. Calculate the inducance of the choke coil for the safe working of the device.

Explanation

In DC circuit :
V = 80 volt
I = 10A
`R=V/I=80/10 = 8 Omega`
In AC circuit:
`R=8Omega`
` E_v= 100 V`
`v= 50 Hz`
L= ?
` I_v= 10 A`
`Z=E_v/I_v = 100/10 =10Omega`
Now `Z=sqrt(R^2+X_L^2)`
`Z = sqrt(R^2+4pi^2v^2L^2)`
On squaring,
`Z^2 =R^2 +4pi^2v^2L^2`
`(10)^2 =(8)^2+4(3.14)^2(50)^2L^2`
`4 xx9.8596xx2500xxL^2 =100 - 64=36`
`L^2 =36/(4xx9.8596xx2500)`
`L = sqrt((36)/(4xx9.8596xx2500))`
`=0.0191H`