Question

An ideal transformer with purely resistive load operates at 12 kV on the primary side. It supplies electrical energy to a number of nearby houses at 120 V. The average rate of energy consumption in the houses served by the transformer is 60 kW. The value of resistive load (Rs) required in the secondary circuit will be ________ mΩ.

Answer 1

Correct Answer: 240

To find the resistive load \( (R_s) \) in the secondary circuit, we can use the relationship between power, voltage, and resistance, along with the principles of an ideal transformer.

Step 1: Determine Secondary Current
First, we need to determine the total power supplied to the houses and use it to find the secondary current. The power equation is:

\[ P = V_s \cdot I_s \]

where \( P = 60 \) kW = 60000 W and \( V_s = 120 \) V. Solving for \( I_s \) (secondary current):

\[ I_s = \frac{P}{V_s} = \frac{60000}{120} = 500 \text{ A} \]

Step 2: Calculate Resistive Load
Now, to find the resistive load \( R_s \), use Ohm's Law \( V = I \cdot R \), where:

\[ R_s = \frac{V_s}{I_s} = \frac{120}{500} = 0.24 \text{ Ω} \]

Convert ohms to milliohms for the final answer:

\[ R_s = 0.24 \times 1000 = 240 \text{ mΩ} \]

Step 3: Verification
The calculated resistive load \( R_s = 240 \text{ mΩ} \) falls within the given range of 240 mΩ. Thus, the solution fits the provided criteria.