Question

A step-down transformer is used to reduce the main supply from $V_1$ volt to $V_2$ volt. The primary coil draws a current $I_1$ A and the secondary coil draws $I_2$ A ($I_1 \lt I_2$). The ratio of input power to output power is

• A. $\frac{V_1 V_2}{I_1 I_2}$
• B. $\frac{V_1 I_1}{V_2 I_2}$
• C. $\frac{I_1 I_2}{V_1 V_2}$
• D. $\frac{V_1 I_2}{V_2 I_1}$

Hint:

Always remember that power is simply voltage multiplied by current ($P = VI$). Therefore, the input power must contain the primary parameters ($V_1 I_1$) in the numerator, and the output power must contain the secondary parameters ($V_2 I_2$) in the denominator.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We are analyzing an electrical step-down transformer converting primary voltage $V_1$ to secondary voltage $V_2$, with corresponding operating currents $I_1$ and $I_2$. We need to write the algebraic ratio expressing input power relative to output power.

Step 2: Key Formula or Approach:
Electric power $P$ delivered or consumed in an alternating current circuit branch is given by the product of the operating voltage and current: $$P = V \times I$$ The input power ($P_{\text{in}}$) corresponds to the primary circuit stage, and the output power ($P_{\text{out}}$) corresponds to the secondary load stage.

Step 3: Detailed Explanation:
Let's write down the independent power equations for both sides of the transformer: 1. Primary side input power: $$P_{\text{in}} = V_1 \cdot I_1$$ 2. Secondary side output power: $$P_{\text{out}} = V_2 \cdot I_2$$ Taking the direct ratio of the input power to the output power yields: $$\text{Ratio} = \frac{P_{\text{in}}}{P_{\text{out}}} = \frac{V_1 I_1}{V_2 I_2}$$ This matches option (B).

Step 4: Final Answer:
The ratio of input power to output power is $\frac{V_1 I_1}{V_2 I_2}$, which corresponds to option (B).