To determine the efficiency of a cell supplying current to an external resistor, we need to analyze the circuit and apply some fundamental concepts of electrical circuits. Let's break this down step-by-step. ### Step 1: Understanding the Circuit We have a cell with an internal resistance (r) of 1Ω and an external resistor (R) of 3Ω. The total resistance in the circuit is the sum of the internal resistance and the external resistance: \[ R_{\text{total}} = R + r = 3Ω + 1Ω = 4Ω \] ### Step 2: Calculating the Current Using Ohm's Law, we can find the current (I) flowing through the circuit. However, we need to know the voltage (V) of the cell to calculate the current. For this example, let's assume the cell has a voltage of V volts. The current can be calculated using the formula: \[ I = \frac{V}{R_{\text{total}}} = \frac{V}{4Ω} \] ### Step 3: Power Supplied by the Cell The power (P) supplied by the cell can be calculated using the formula: \[ P_{\text{cell}} = V \cdot I = V \cdot \frac{V}{4Ω} = \frac{V^2}{4Ω} \] ### Step 4: Power Delivered to the External Resistor The power delivered to the external resistor (P_R) can be calculated using the formula: \[ P_R = I^2 \cdot R = \left(\frac{V}{4Ω}\right)^2 \cdot 3Ω \] Calculating this gives: \[ P_R = \frac{V^2}{16Ω^2} \cdot 3Ω = \frac{3V^2}{16Ω} \] ### Step 5: Calculating Efficiency Efficiency (η) is defined as the ratio of the power delivered to the external resistor to the total power supplied by the cell: \[ \eta = \frac{P_R}{P_{\text{cell}}} \times 100\% \] Substituting the values we calculated: \[ \eta = \frac{\frac{3V^2}{16Ω}}{\frac{V^2}{4Ω}} \times 100\% \] Simplifying this expression: \[ \eta = \frac{3V^2}{16Ω} \cdot \frac{4Ω}{V^2} \times 100\% = \frac{3 \cdot 4}{16} \times 100\% = \frac{12}{16} \times 100\% = 75\% \] ### Conclusion Thus, the efficiency of the cell is **75%**, which corresponds to option D. ### Explanation of Other Options - **Option A (25%)**: This would imply that only a quarter of the power is being used effectively, which is not supported by our calculations. - **Option B (33%)**: This suggests that one-third of the power is used effectively, which is also not consistent with our findings. - **Option C (50%)**: This would mean half of the power is used effectively, which is lower than our calculated efficiency. ### Revision Summary - The total resistance in the circuit is the sum of internal and external resistances. - The current can be calculated using Ohm's Law. - Power supplied by the cell and power delivered to the external resistor are calculated using the respective formulas. - Efficiency is the ratio of power delivered to the external resistor to the total power supplied by the cell, expressed as a percentage. By understanding these concepts and calculations, you can effectively analyze similar problems in the future.