Question 1 CEL02 - Chief Engineer - Limited (Alt)

The Correct Answer is A ### 1. Explanation for Option A (15 ohms) The circuit described in figure "B" (Illustration EL-0032, typically representing a combined series-parallel circuit) shows that resistors $R_2$ and $R_3$ are connected in parallel, and this parallel combination is connected in series with resistor $R_1$. **Given Values:** $R_1 = 10 \text{ ohms}$ $R_2 = 10 \text{ ohms}$ $R_3 = 10 \text{ ohms}$ **Step 1: Calculate the equivalent resistance of the parallel combination ($R_{p}$) for $R_2$ and $R_3$.** The formula for two resistors in parallel is: $$R_p = \frac{R_2 \times R_3}{R_2 + R_3}$$ Substituting the values: $$R_p = \frac{10 \text{ ohms} \times 10 \text{ ohms}}{10 \text{ ohms} + 10 \text{ ohms}}$$ $$R_p = \frac{100 \text{ ohms}^2}{20 \text{ ohms}}$$ $$R_p = 5 \text{ ohms}$$ **Step 2: Calculate the total resistance ($R_{total}$).** The total resistance is the sum of $R_1$ (series resistor) and the equivalent parallel resistance ($R_p$): $$R_{total} = R_1 + R_p$$ $$R_{total} = 10 \text{ ohms} + 5 \text{ ohms}$$ $$R_{total} = 15 \text{ ohms}$$ Therefore, the total resistance is 15 ohms. ### 2. Explanation for Why Other Options are Incorrect **B) 20 ohms:** This value would be correct if $R_1$ and $R_2$ were in series ($R_1 + R_2 = 10 + 10 = 20 \text{ ohms}$) and $R_3$ was ignored, or if $R_1$ were in series with the parallel combination of two 20-ohm resistors. It does not reflect the correct calculation for the given circuit. **C) 25 ohms:** This value suggests an incorrect calculation, possibly if $R_1$ (10 $\Omega$) were in series with a parallel combination that somehow resulted in 15 $\Omega$. There is no standard arrangement of these three 10 $\Omega$ resistors that yields 25 ohms. **D) 30 ohms:** This value would be the total resistance only if all three resistors ($R_1$, $R_2$, and $R_3$) were connected in **series** ($R_{total} = R_1 + R_2 + R_3 = 10 + 10 + 10 = 30 \text{ ohms}$). Since the circuit in Figure "B" includes a parallel segment ($R_2$ and $R_3$), this option is incorrect.