>>216366474
Circuit Analysis
This is a series-parallel DC circuit with a 20 V source, where R1 (20 Ω) is in series with the parallel combination of R2 (30 Ω) and R3 (60 Ω).
Step 1: Calculate Equivalent Resistance (RT)
The parallel resistance of R2 and R3 is calculated using the formula for two resistors in parallel:
$ R_{parallel} = \frac{R_2 \times R_3}{R_2 + R_3} = \frac{30 \times 60}{30 + 60} = \frac{1800}{90} = 20 \, \Omega $.
Total resistance RT is R1 plus the parallel equivalent:
$ R_T = R_1 + R_{parallel} = 20 + 20 = 40 \, \Omega $.
Step 2: Calculate Total Current (IT)
Using Ohm's Law: $ I_T = \frac{V}{R_T} = \frac{20}{40} = 0.5 \, \mathrm{A} $.
Step 3: Calculate Currents Through Each Resistor
Current through R1 (series with total current): $ I_{R1} = I_T = 0.5 \, \mathrm{A} $.
Voltage across the parallel branch: $ V_{parallel} = I_T \times R_{parallel} = 0.5 \times 20 = 10 \, \mathrm{V} $.
(Alternatively, voltage across R1 is $ I_T \times R_1 = 0.5 \times 20 = 10 \, \mathrm{V} $, so the remaining voltage across the parallel branch is $ 20 - 10 = 10 \, \mathrm{V} $.)
Current through R2: $ I_{R2} = \frac{V_{parallel}}{R_2} = \frac{10}{30} \approx 0.333 \, \mathrm{A} $ (or exactly $ \frac{1}{3} \, \mathrm{A} $).
Current through R3: $ I_{R3} = \frac{V_{parallel}}{R_3} = \frac{10}{60} \approx 0.167 \, \mathrm{A} $ (or exactly $ \frac{1}{6} \, \mathrm{A} $).
(Verification: $ I_{R2} + I_{R3} = 0.333 + 0.167 = 0.5 \, \mathrm{A} $, matching IT.)
Step 4: Calculate Voltage Drops Across Each Resistor
Voltage drop across R1: $ V_{R1} = I_{R1} \times R_1 = 0.5 \times 20 = 10 \, \mathrm{V} $.
Voltage drop across R2: $ V_{R2} = I_{R2} \times R_2 = 0.333 \times 30 = 10 \, \mathrm{V} $ (or $ V_{parallel} = 10 \, \mathrm{V} $).
Voltage drop across R3: $ V_{R3} = I_{R3} \times R_3 = 0.167 \times 60 = 10 \, \mathrm{V} $ (or $ V_{parallel} = 10 \, \mathrm{V} $).
(Verification: Total voltage = $ V_{R1} + V_{parallel} = 10 + 10 = 20 \, \mathrm{V} $.)
10/31/2025, 6:28:07 PM
No.216364968
[Report]
>>216365065
>>216365554
>>216365587
>>216366564
10/31/2025, 7:35:06 PM
No.216366848
[Report]
>>216366886
>>216366892
>>216366941
>>216366987
10/31/2025, 7:53:28 PM
No.216367322
[Report]
>>216367358
>>216367384
