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
Step 1: Resistors R_1 and R_2 are connected in parallel, so the voltage V across both is the same. Current through R_1: I_1 = (V)/(R_1) Current through R_2: I_2 = (V)/(R_2) I_1 = (V)/(R_1) I_2 = (V)/(R_2) Step 2: Total current I = I_1 + I_2 I = (V)/(R_1) + (V)/(R_2) = V ( (1)/(R_1) + (1)/(R_2) ) Step 3: For equivalent resistance R_eq, I = (V)/(R_eq) (1)/(R_eq) = (1)/(R_1) + (1)/(R_2) Step 4: Common denominator R_1 R_2 (1)/(R_eq) = (R_2)/(R_1 R_2) + (R_1)/(R_1 R_2) = (R_1 + R_2)/(R_1 R_2) Step 5: Take reciprocal R_eq = (R_1 R_2)/(R_1 + R_2) This matches option (a). (a)