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ScanSolve AI Answer
Here's the solution to your circuit problem: a) Step 1: Calculate the equivalent resistance of the parallel combination (R_p) of R_2, R_3, and R_4. (1)/(R_p) = (1)/(R_2) + (1)/(R_3) + (1)/(R_4) (1)/(R_p) = (1)/(15 \, ) + (1)/(20 \, ) + (1)/(30 \, ) To add these fractions, find a common denominator, which is 60. (1)/(R_p) = (4)/(60 \, ) + (3)/(60 \, ) + (2)/(60 \, ) (1)/(R_p) = (4+3+2)/(60 \, ) = (9)/(60 \, ) R_p = (60)/(9) \, = (20)/(3) \, Step 2: Calculate the total resistance (R_T) of the circuit. R_1 is in series with R_p. R_T = R_1 + R_p R_T = 10 \, + (20)/(3) \, R_T = (30)/(3) \, + (20)/(3) \, = (50)/(3) \, The total resistance of the circuit is (50)/(3) \, . (50)/(3) \, ≈ 16.67 \, b) Step 3: Calculate the total current (I_T) flowing from the source using Ohm's Law (I = (V)/(R)). I_T = (V)/(R_T) I_T = (12 \, V)/(50)3 \, I_T = (12 × 3)/(50) \, A = (36)/(50) \, A = (18)/(25) \, A The total current flowing from the source is (18)/(25) \, A. (18)/(25) \, A = 0.72 \, A c) Step 4: Calculate the voltage (V_p) across the parallel combination (R_p). This is the voltage across R_2, R_3, and R_4. V_p = I_T × R_p V_p = (18)/(25) \, A × (20)/(3) \, V_p = (18 × 20)/(25 × 3) \, V = (6 × 20)/(25) \, V = (120)/(25) \, V = (24)/(5) \, V Step 5: Calculate the current (I_3) flowing through the 20 \, resistor (R_3) using Ohm's Law. I_3 = (V_p)/(R_3) I_3 = (24)/(5) \, V20 \, I_3 = (24)/(5 × 20) \, A = (24)/(100) \, A = (6)/(25) \, A The current flowing through the 20 \, resistor is (6)/(25) \, A. (6)/(25) \, A = 0.24 \, A 3 done, 2 left today. You're making progress.