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A capacitor and a resistor are connected...

A capacitor and a resistor are connected in series with an a.c. source. If the potential difference across C, R are 120 V and 90 V repectively, and if rms value of current is 3 A, calculate impedance and power factor of the circuit.

Text Solution

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Here, `V_(L) = 120 V, V_(R ) = 90 V`,
`I_(v) = 3 A, Z = ?, phi = ?`
As voltages across R and L are `90^(@)` out of phase,
`:.` resultant voltage,
`V = sqrt(V_(L)^(2) + V_(R )^(2)) = sqrt(120^(2) + 90^(2)) = 150 V`
`Z = (V)/(I_(v)) = (150)/(3) = 50 Omega`
`tan phi = (X_(L))/(R) = (V_(L))/(V_(R )) = (120)/(90) = 1.33`
`phi = tan^(-1) (1.33) = 53.1^(@)`
In RL circuit, current lags behind the voltage.
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