Final answer:
To determine the capacitance in an RC circuit with known power absorption and voltage, calculate the resistance using power formulas, then find the voltage across the capacitor and use these values to calculate capacitive reactance and finally capacitance. The energy stored in the capacitor can be found using the energy equation for capacitors.
Step-by-step explanation:
To find the value of the capacitor (C) in a series RC circuit when a 400 volt, 50 hertz supply is applied, and given that the power absorbed by the resistor is 5000 watts at 150 volts, we can use the formula for power in an AC circuit, which is P = V^2/R, where P is the power, V is the voltage across the resistor, and R is the resistance. We can solve for R since we know the power and voltage:
R = V^2 / P = (150^2) / 5000 = 4.5 ohms.
Now, since we know the supply voltage (V_s) is 400 volts and the voltage across R is 150 volts, we can apply Kirchhoff's voltage law to determine the voltage across the capacitor (V_C):
V_C = sqrt(V_s^2 - V_R^2) = sqrt(400^2 - 150^2)
Once V_C is found, we can calculate the capacitive reactance (X_C) using the formula X_C = V_C / I, where I is the current which can be calculated by I = V_R / R. Finally, we can find the capacitance (C) using the formula C = 1 / (2πfX_C), where f is the frequency.
The energy stored in the capacitor is given by the equation E = 1/2 * C * V_C^2.