An ideal choke draws a current of 8 A when connected to an AC supply of 100 V, 50 Hz. A pure resistor draws a current of 10 A when connected to the same source. The ideal choke and the resistor are connected in series and then connected to the AC source of 150 V, 40 Hz. The current in the circuit becomes

Options

A. `(15)/(sqrt(2))`
B. `8A`
C. `18A`
D. `10A`

Answer

A

Explanation

An ideal choke has zero ohmic resistance

The inductive reactance of a choke is
`X_(L)=2pivL`
`:.(100)/(8)=2pixx50xxL`
`L=(1)/(8pi)H`

The resistance of the resistor is
`R=(100)/(10)=10Omega`
`L=(1)/(8pi)H`

Now, the inductive reactance of the choke is `X_(L)^(.)=2piv.L=2pixx40xx1/(8pi)=10Omega`
The impedence of the circuit is
`Z=sqrt(R^(2)+X_(L)^(.2))=sqrt((10)^(2)+(10)^(2))=10sqrt(2)Omega`
Current in the circuit is
`I=(V)/(Z)=(150)/(10sqrt(2))=(15)/(sqrt(2))A`