To solve the problem involving a steel-cored reactor and a non-reactive resistor connected in series to a 150V AC supply, we need to analyze the circuit step by step. We know the current flowing through the circuit is 3.75A, and the potential differences across the reactor and resistor are 120V and 60V, respectively. Let's break this down to find the core loss in the reactor and its equivalent series resistance.
Understanding the Circuit Components
In this circuit, we have two main components:
- Reactor: This is an inductive component, which means it has reactance in addition to resistance. The DC resistance of the reactor is given as 4.5 ohms.
- Resistor: This is a non-reactive component, meaning it only has resistance and no reactance.
Calculating the Total Voltage and Impedance
The total voltage supplied is 150V, which is the sum of the voltages across the reactor and the resistor:
V_total = V_reactor + V_resistor
Substituting the known values:
150V = 120V + 60V
This confirms our voltage readings are correct.
Finding the Equivalent Series Resistance
The total current flowing through the circuit is 3.75A. We can find the equivalent series resistance (R_eq) using Ohm's Law:
V = I × R
For the entire circuit, we can express it as:
R_eq = V_total / I
Substituting the known values:
R_eq = 150V / 3.75A = 40 ohms
Calculating the Resistance of the Resistor
We know the voltage across the resistor is 60V. Using Ohm's Law again:
R_resistor = V_resistor / I
Substituting the values:
R_resistor = 60V / 3.75A = 16 ohms
Finding the Reactance of the Reactor
Now, we can find the reactance (X) of the reactor. The voltage across the reactor is 120V:
X_reactor = V_reactor / I
Substituting the values:
X_reactor = 120V / 3.75A = 32 ohms
Calculating Core Loss in the Reactor
Core loss in the reactor can be calculated using the formula:
Core Loss (P) = I² × R_dc
Where R_dc is the DC resistance of the reactor. Substituting the values:
P = (3.75A)² × 4.5 ohms
P = 14.0625 × 4.5 = 63.28125W
Finalizing the Equivalent Series Resistance
To find the total equivalent series resistance, we need to add the DC resistance of the reactor to the resistance of the resistor:
R_eq_total = R_resistor + R_dc
R_eq_total = 16 ohms + 4.5 ohms = 20.5 ohms
Summary of Results
In summary, the core loss in the reactor is approximately 63.28W, and the equivalent series resistance is 20.5 ohms. These calculations help us understand the behavior of the circuit under the given conditions.
