Let's break down the problem step by step. ## Given Data - \( E = 14.6\,V \) - \( R_1 = 273\,\Omega \) - \( R_2 = 256\,\Omega \) - \( R_3 = 325\,\Omega \) Assuming the resistors are in series (which is typical unless otherwise shown): ### 1. **Total Resistance** \[ R_{total} = R_1 + R_2 + R_3 = 273 + 256 + 325 = 854\,\Omega \] ### 2. **Current in the Circuit** \[ I = \frac{E}{R_{total}} = \frac{14.6}{854} = .00171\,A = 1.71\,mA \] --- ## 3. **Potential Differences Across Each Resistor** \[ V_{R_1} = I \cdot R_1 = .00171 \times 273 = 4.67\,V \] \[ V_{R_2} = I \cdot R_2 = .00171 \times 256 = 4.38\,V \] \[ V_{R_3} = I \cdot R_3 = .00171 \times 325 = 5.56\,V \] --- ## 4. **Potential Differences** Assuming: - \( A \) is at the positive terminal of the battery, - \( B \) is after \( R_1 \), - \( C \) is after \( R_2 \), - \( D \) is after \( R_3 \) (back to the negative terminal). ### (a) \( V_A - V_B \) (Across \( R_1 \)) \[ V_A - V_B = V_{R_1} = 4.67\,V \] ### (b) \( V_B - V_C \) (Across \( R_2 \)) \[ V_B - V_C = V_{R_2} = 4.38\,V \] ### (c) \( V_C - V_D \) (Across \( R_3 \)) \[ V_C - V_D = V_{R_3} = 5.56\,V \] ### (d) \( V_A - V_C \) (Across \( R_1 + R_2 \)) \[ V_A - V_C = V_{R_1} + V_{R_2} = 4.67 + 4.38 = 9.05\,V \] --- ## **Summary Table** | Part | Potential Difference | Value (V) | |------|---------------------|-----------| | (a) | \( V_A - V_B \) | 4.67 | | () | \( V_B - V_C \) | 4.38 | | (c) | \( V_C - V_D \) | 5.56 | | (d) | \( V_A - V_C \) | 9.05 | --- If you have a diagram or a different configuration, let me know! But with the standard series arrangement, these are the answers.