Capacitance of the capacitor, C = 100 μF = 100 x 10^-6 F = 10⁻⁴ F

Resistance of the resistor, R = 40 Ω

Supply voltage, V = 110 V

Ans (a).

Frequency of oscillations, ν= 60 Hz

Angular frequency, ω = 2π ν = 2π x 60 rad/s =120π rad/s

For a RC circuit, we have the relation for impedance as: Z = √(R² +1/ω²c²)

Peak voltage, V₀ = V√2 = 110√2. Maximum current is given as:

I₀= V₀ /Z  =  V₀/√(R² +1/ω²c²)

=110 √2 / √(R² +1/ω²c²)

=110 √2 / √(40² +1/(120π)²(10⁻⁴)²)

=3.24A

Ans (b).

In a capacitor circuit, the voltage lags behind the current by a phase angle of φ. This angle is given by the relation:

tan φ =(1/ωC)/R = 1/ωCR

=1/(120 π10⁻⁴x 40)

= 0.6635

Therefore, φ =tan⁻¹ (0.6635) = 33.56º

= 33.56π/180 rad

Therefore ,Time lag = φ/ω = 33.56 π/(180 x 120 π) = 1.55 x 10⁻³ s

=1.55 ms

Hence, the time lag between maximum current and maximum voltage is 1.55 ms.