When an AC source of `emf e=E_(0) sin(100t)` is connected across a circuit i in the circuit, the phase difference between the emf e and the current i in the circuit is observed to be `(pi//4)`, as shown in the diagram. If the circuit consists possibly only of R-C or R-L or L-C in series, find the relationship between the two elements

Options

A. `R = 1 kOmega, C = 10 muF`
B. `R = 1 kOmega, C = 1muF`
C. `R =1 kOmega, L = 10 H`
D. `R = 1kOmega, L = 1 H`

Answer

A

Explanation

The current is leading the voltage in the gievn graph and the phase difference is not equal to 90°. So, we can conclude that resistor and capacitor can be the probable elements of the circuit.
If we take R to be the resistance and C to be the capacitance and be the phase difference between current and applied voltage.
For RC circuit,
`tan phi = X_( e)/R`
For `phi = 45^(@), tan phi = 1`
`X_( c) = R rArr 1/(omegac) = R`
Given that, `R = 1 kOmega, w = 100`
Substituting in the above equation, we get
`1/(100 C) = 1 xx 10^(3)`
`C = 10 muF`