Question

A series LCR circuit containing a resistance of 120 Ω has angular resonance frequency 4 × 10⁵ rad s^-1. At resonance the voltage across resistance and inductance are 60 V and 40 V respectively. At what frequency the current in the circuit lags the voltage by 45°. Give answer in ______ × 10⁵ rad s^-1.

Options

• 5

• 6

• 7

• 8

Answer 1

A series LCR circuit containing a resistance of 120 Ω has angular resonance frequency 4 × 10⁵ rad s^-1. At resonance the voltage across resistance and inductance are 60 V and 40 V respectively. At what frequency the current in the circuit lags the voltage by 45°. Give answer in 8 × 10⁵ rad s^-1.

Explanation:

At resonance reactance = 0

I = `"V"/"R" = 60/120 = 1/2` Amp

V_L = I × X_L = I × ωL

∴ L = `"V"_"L"/("I"omega)`        ...(i)

ω₀ = `1/sqrt"LC"`

C = `1/("L"omega_0^2)`       ...(ii)

Calculate L and C from (i) and (ii) current will lag the applied voltage by 45°

if tan 45° = `(omega"L"-1/(omega"c"))/"R"`

 Solve for ω 

ω = 8 × 10⁵ rad/s.