The power absorbed by the resistor in the given problem 16 W. This can be gotten by solving series of equations.
How to solve the problem?
A controlled half-wave rectifier circuit can be used to produce an average voltage of 40 V across a 100Ω load resistor from a 120 Vrms 60 Hz ac source. The required delay angle α can be determined using the following equation:
α = cos⁻¹(Vd/Vm)
where:
Vd is the desired average voltage (40 V)
Vm is the peak voltage of the ac source (120 Vrms * √2 = 169.7 V)
Plugging in the values, we get:
α = cos⁻¹(40 V / 169.7 V) ≈ 82.9°
To achieve this delay angle, a triac can be used as the switching element in the half-wave rectifier circuit. The triac's gate trigger signal can be controlled by a phase-shifting circuit that generates a voltage waveform with a leading edge delay of α.
The power absorbed by the resistor can be calculated using the following equation:
P = Vd² / R
where:
Pd is the average power
Vd is the desired average voltage (40 V)
R is the load resistance (100Ω)
Plugging in the values, we get:
P = (40 V)² / 100Ω = 16 W