Part 1: Equivalent Resistance in a Parallel Circuit

Here's a step-by-step solution for the problem shown in the image. Part 1: Equivalent Resistance in a Parallel Circuit The formula for the equivalent resistance (R_eq) of resistors connected in parallel is given by: (1)/(R_eq) = (1)/(R_1) + (1)/(R_2) + (1)/(R_3) From the image, the given resistance values are R_1 = 4 \, , R_2 = 6 \, , and R_3 = 3 \, . Step 1: Substitute the given resistance values into the formula. (1)/(R_eq) = (1)/(4 \, ) + (1)/(6 \, ) + (1)/(3 \, ) Step 2: Find a common denominator for the fractions. The least common multiple (LCM) of 4, 6, and 3 is 12. (1)/(R_eq) = (3)/(12 \, ) + (2)/(12 \, ) + (4)/(12 \, ) Step 3: Add the fractions. (1)/(R_eq) = (3+2+4)/(12 \, ) (1)/(R_eq) = (9)/(12 \, ) Step 4: Simplify the fraction and take the reciprocal to find R_eq. (1)/(R_eq) = (3)/(4 \, ) R_eq = (4)/(3) \, As a decimal, this is approximately: R_eq ≈ 1.33 \, The student's calculation for the sum of fractions ((13)/(72)) was incorrect, leading to an incorrect final resistance value. The correct equivalent resistance is (4)/(3) \, or 1.33 \, . Part 2: Voltage in a Parallel Circuit The image states: V_T = V_1 = V_2 and then V_T = 12 = 6. In a parallel circuit, the voltage across each resistor is the same as the total voltage supplied by the source. Therefore, the statement V_T = V_1 = V_2 (and also V_3) is correct. However, the statement V_T = 12 = 6 is contradictory. It implies that the total voltage is simultaneously 12 V and 6 V, which is not possible. Without additional context from the original problem, it is not possible to determine the correct total voltage. Send me the next one 📸