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.
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Here's the solution to the physics problem: Given: Voltage of the battery (V) = 12 \, V Resistance R_1 = 2 \, Resistance R_2 = 4 \, Resistance R_3 = 6 \, a) Total resistance of the circuit Step 1: Calculate the equivalent resistance of R_2 and R_3 which are connected in parallel. The formula for two resistors in parallel is (1)/(R_p) = (1)/(R_2) + (1)/(R_3). (1)/(R_p) = (1)/(4 \, ) + (1)/(6 \, ) To add these fractions, find a common denominator, which is 12. (1)/(R_p) = (3)/(12 \, ) + (2)/(12 \, ) (1)/(R_p) = (3+2)/(12 \, ) (1)/(R_p) = (5)/(12 \, ) R_p = (12)/(5) \, R_p = 2.4 \, Step 2: Calculate the total resistance of the circuit. The equivalent resistance R_p is in series with R_1. The formula for resistors in series is R_total = R_1 + R_p. R_total = 2 \, + 2.4 \, R_total = 4.4 \, The total resistance of the circuit is 4.4 . b) Total current flowing from the battery Step 1: Use Ohm's Law to find the total current. Ohm's Law states V = I R, so I_total = (V)/(R_total). I_total = 12 \, V4.4 \, I_total = (120)/(44) \, A I_total = (30)/(11) \, A I_total ≈ 2.73 \, A The total current flowing from the battery is 2.73 A. c) Current flowing through R_2 Step 1: Calculate the potential difference (voltage) across the parallel combination (R_p). The total current I_total flows through R_1 and then through the parallel combination R_p. So, the voltage across R_p is V_p = I_total × R_p. V_p = (30)/(11) \, A × 2.4 \, V_p = (30)/(11) × (12)/(5) \, V V_p = (6 × 12)/(11) \, V V_p = (72)/(11) \, V V_p ≈ 6.55 \, V Step 2: Calculate the current flowing through R_2. Using Ohm's Law for R_2: I_2 = (V_p)/(R_2). I_2 = (72)/(11) \, V4 \, I_2 = (72)/(11 × 4) \, A I_2 = (18)/(11) \, A I_2 ≈ 1.64 \, A The current flowing through R_2 is 1.64 A. d) Potential difference across R_3 Step 1: Recognize that resistors in parallel have the same potential difference across them. Since R_2 and R_3 are in parallel, the potential difference across R_3 (V_3) is the same as the potential difference across R_2 and the parallel combination (V_p). V_3 = V_p V_3 = (72)/(11) \, V V_3 ≈ 6.55 \, V The potential difference across R_3 is 6.55 V. Last free one today — make it count tomorrow, or type /upgrade for unlimited.