Looking at this fourth circuit, I can see it's a parallel circuit with two resistors (R1 and R2) connected to a voltage source. The values are given as R1 = 5Ω and R2 = 10Ω, with a total voltage of 30V.
To solve this circuit, I need to:
1. Calculate the total resistance (RT)
2. Calculate the total current (IT) using Ohm's Law
3. Calculate the current through each resistor
4. Calculate the power for each resistor
Let me calculate these values:
1. Total Resistance (RT): In a parallel circuit, 1/RT = 1/R1 + 1/R2
- 1/RT = 1/5Ω + 1/10Ω = 2/10Ω + 1/10Ω = 3/10Ω
- RT = 10/3Ω ≈ 3.33Ω
2. Total Current (IT): Using Ohm's Law (V = IR), IT = V/RT = 30V/(10/3Ω) = 30V × 3/10 = 9A
3. Current through each resistor:
- I1 = V/R1 = 30V/5Ω = 6A
- I2 = V/R2 = 30V/10Ω = 3A
4. Power for each resistor: P = V²/R or P = VI
- P1 = V²/R1 = (30V)²/5Ω = 900/5 = 180W
- P2 = V²/R2 = (30V)²/10Ω = 900/10 = 90W
Now I have solved all four circuits. Let me summarize the solutions for each circuit.
Circuit 1 (Series, R1=5Ω, R2=5Ω, V=20V):
- RT = 10Ω
- IT = 2A
- V1 = 10V, V2 = 10V
- P1 = 20W, P2 = 20W
Circuit 2 (Series, R1=5Ω, R2=10Ω, V=30V):
- RT = 15Ω
- IT = 2A
- V1 = 10V, V2 = 20V
- P1 = 20W, P2 = 40W
Circuit 3 (Parallel, R1=5Ω, R2=5Ω, V=20V):
- RT = 2.5Ω
- IT = 8A
- I1 = 4A, I2 = 4A
- P1 = 80W, P2 = 80W
Circuit 4 (Parallel, R1=5Ω, R2=10Ω, V=30V):
- RT = 10/3Ω ≈ 3.33Ω
- IT = 9A
- I1 = 6A, I2 = 3A
- P1 = 180W, P2 = 90W
These are the complete solutions for all four circuits shown in the worksheet.
Parent Tip: Review the logic above to help your child master the concept of series circuits worksheet answers.
