This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
B Step 1: Calculate the equivalent capacitance of the top series branch. The capacitors are 3, 6, and 2 in series. For capacitors in series, the reciprocal of the equivalent capacitance is the sum of the reciprocals of individual capacitances. (1)/(C_top) = (1)/(3) + (1)/(6) + (1)/(2) (1)/(C_top) = (2)/(6) + (1)/(6) + (3)/(6) (1)/(C_top) = (2+1+3)/(6) = (6)/(6) = (1)/(1) C_top = 1 Step 2: Calculate the equivalent capacitance of the bottom series branch. The capacitors are 4 and 4 in series. (1)/(C_bottom) = (1)/(4) + (1)/(4) (1)/(C_bottom) = (2)/(4) = (1)/(2) C_bottom = 2 Step 3: Calculate the equivalent capacitance of the parallel combination of the top and bottom branches. For capacitors in parallel, the equivalent capacitance is the sum of individual capacitances. C_parallel = C_top + C_bottom C_parallel = 1 + 2 C_parallel = 3 Step 4: Calculate the total effective capacitance of the circuit. The 2 capacitor on the left, C_parallel, and the 2 capacitor on the right are all in series. (1)/(C_effective) = (1)/(2) + (1)/(C_parallel) + (1)/(2) (1)/(C_effective) = (1)/(2) + (1)/(3) + (1)/(2) Find a common denominator, which is 6. (1)/(C_effective) = (3)/(6) + (2)/(6) + (3)/(6) (1)/(C_effective) = (3+2+3)/(6) = (8)/(6) = (4)/(3) C_effective = (3)/(4) C_effective = 0.75 The effective capacitance is 0.75. This matches option B. The final answer is 0.75 F. Send me the next one 📸