- Step 1: Calculate the total resistance (R_T).
- R_2 and R_4 are in parallel: R_24 = (R_2 * R_4) / (R_2 + R_4) = (10 Ω * 12 Ω) / (10 Ω + 12 Ω) = 120 / 22 ≈ 5.45 Ω.
- R_13 = R_1 + R_24 = 15 Ω + 5.45 Ω = 20.45 Ω.
- R_13 and R_5 are in parallel: R_135 = (R_13 * R_5) / (R_13 + R_5) = (20.45 Ω * 10 Ω) / (20.45 Ω + 10 Ω) ≈ 204.5 / 30.45 ≈ 6.72 Ω.
- R_T = R_135 + R_3 = 6.72 Ω + 30 Ω = 36.72 Ω.
- Step 2: Calculate the main line current (I_T).
- I_T = V_T / R_T = 100 V / 36.72 Ω ≈ 2.72 A.
- Step 3: Calculate voltage drops and branch currents.
- Voltage across R_3: V_3 = I_T * R_3 = 2.72 A * 30 Ω = 81.6 V.
- Voltage across the parallel combination (R_135): V_135 = V_T - V_3 = 100 V - 81.6 V = 18.4 V.
- Current through R_5: I_5 = V_135 / R_5 = 18.4 V / 10 Ω = 1.84 A.
- Current through R_13: I_13 = V_135 / R_13 = 18.4 V / 20.45 Ω ≈ 0.90 A.
- Voltage across R_1: V_1 = I_13 * R_1 = 0.90 A * 15 Ω = 13.5 V.
- Voltage across R_24: V_24 = I_13 * R_24 = 0.90 A * 5.45 Ω ≈ 4.91 V.
- Current through R_2: I_2 = V_24 / R_2 = 4.91 V / 10 Ω ≈ 0.491 A.
- Current through R_4: I_4 = V_24 / R_4 = 4.91 V / 12 Ω ≈ 0.409 A.
- Summary of currents:
- I_T = 2.72 A
- I_1 = I_13 = 0.90 A
- I_2 = 0.491 A
- I_3 = I_T = 2.72 A
- I_4 = 0.409 A
- I_5 = 1.84 A
- Summary of voltages:
- V_1 = 13.5 V
- V_2 = 4.91 V
- V_3 = 81.6 V
- V_4 = 4.91 V
- V_5 = 18.4 V
Parent Tip: Review the logic above to help your child master the concept of series parallel resistor worksheet.
