Series Circuit Problems online exercise for - Free Printable

Let’s work through each circuit problem one by one. Since all are series circuits, we remember:

- Current (I) is the same everywhere in a series circuit.
- Total voltage = sum of voltages across each resistor.
- Total resistance = sum of all resistances: R_T = R₁ + R₂ + ...
- Use Ohm’s Law: V = I × R → so I = V/R, and R = V/I.

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Circuit 1 (Top Left):

Given:
- Battery = 90V
- R₁ = 10Ω, R₂ = 20Ω

Step 1: Find total resistance
R_T = R₁ + R₂ = 10 + 20 = 30Ω

Step 2: Find total current (same everywhere in series)
I_T = V / R_T = 90V / 30Ω = 3A

So I₁ = I₂ = I_T = 3A

Step 3: Find voltage drops
V₁ = I × R₁ = 3A × 10Ω = 30V
V₂ = I × R₂ = 3A × 20Ω = 60V

Check: 30V + 60V = 90V ✔

Answers for Circuit 1:
R_T = 30Ω, I_T = 3A
I₁ = 3A, I₂ = 3A
V₁ = 30V, V₂ = 60V

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Circuit 2 (Top Right):

Given:
- Battery = 60V
- R₁ = 6Ω, R₂ = 14Ω, R₃ = 10Ω

Step 1: Total resistance
R_T = 6 + 14 + 10 = 30Ω

Step 2: Total current
I_T = 60V / 30Ω = 2A

All currents equal: I₁ = I₂ = I₃ = 2A

Step 3: Voltage drops
V₁ = 2A × 6Ω = 12V
V₂ = 2A × 14Ω = 28V
V₃ = 2A × 10Ω = 20V

Check: 12 + 28 + 20 = 60V ✔

Answers for Circuit 2:
R_T = 30Ω, I_T = 2A
I₁ = 2A, I₂ = 2A, I₃ = 2A
V₁ = 12V, V₂ = 28V, V₃ = 20V

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Circuit 3 (Middle Left):

Given:
- Battery = 75V
- R₁ = 10Ω
- Current through circuit = 5A (shown as “5a”)
- Voltage across R₂ = 25V (shown as “25v”)

Since it’s series, current is same everywhere → I₂ = 5A

Step 1: Find V₁ (voltage across R₁)
V₁ = I × R₁ = 5A × 10Ω = 50V

Step 2: Check total voltage
V_total = V₁ + V₂ = 50V + 25V = 75V ✔ matches battery

Step 3: Find R₂
R₂ = V₂ / I = 25V / 5A = 5Ω

Answers for Circuit 3:
V₁ = 50V, I₂ = 5A, R₂ = 5Ω

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Circuit 4 (Middle Right):

Given:
- R₁ = 5Ω, R₂ = 15Ω
- Current = 5A (shown as “5a”)

Step 1: Total resistance
R_T = 5 + 15 = 20Ω

Step 2: Total voltage
V_T = I × R_T = 5A × 20Ω = 100V

Step 3: Voltage drops
V₁ = 5A × 5Ω = 25V
V₂ = 5A × 15Ω = 75V

Check: 25 + 75 = 100V ✔

Answers for Circuit 4:
V₁ = 25V, V₂ = 75V, V_T = 100V

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Circuit 5 (Bottom Left):

Given:
- Battery = 20V
- R₁ = 5Ω, R₂ = 3Ω, R₃ = 2Ω

Step 1: Total resistance
R_T = 5 + 3 + 2 = 10Ω

Step 2: Total current
I_T = 20V / 10Ω = 2A

All currents = 2A

Step 3: Voltage drops
V₁ = 2A × 5Ω = 10V
V₂ = 2A × 3Ω = 6V
V₃ = 2A × 2Ω = 4V

Check: 10 + 6 + 4 = 20V ✔

Answers for Circuit 5:
R_T = 10Ω, I_T = 2A
V₁ = 10V, V₂ = 6V, V₃ = 4V

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Circuit 6 (Bottom Right):

Given:
- Battery = 40V
- R₃ = 10Ω, voltage across R₃ = 20V (shown as “20v”)
- Voltage across R₂ = 10V (shown as “10v”)

Step 1: Find current through R₃
I₃ = V₃ / R₃ = 20V / 10Ω = 2A

In series, current is same everywhere → I₁ = I₂ = I₃ = 2A

Step 2: Find V₁ (voltage across R₁)
Total voltage = V₁ + V₂ + V₃
40V = V₁ + 10V + 20V → V₁ = 40 - 30 = 10V

Step 3: Find R₁ and R₂
R₁ = V₁ / I = 10V / 2A = 5Ω
R₂ = V₂ / I = 10V / 2A = 5Ω

Answers for Circuit 6:
I₃ = 2A, I₁ = 2A, V₁ = 10V
R₁ = 5Ω, R₂ = 5Ω

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Final Answer:
Circuit 1: R_T=30Ω, I_T=3A, I₁=3A, I₂=3A, V₁=30V, V₂=60V
Circuit 2: R_T=30Ω, I_T=2A, I₁=2A, I₂=2A, I₃=2A, V₁=12V, V₂=28V, V₃=20V
Circuit 3: V₁=50V, I₂=5A, R₂=5Ω
Circuit 4: V₁=25V, V₂=75V, V_T=100V
Circuit 5: R_T=10Ω, I_T=2A, V₁=10V, V₂=6V, V₃=4V
Circuit 6: I₃=2A, I₁=2A, V₁=10V, R₁=5Ω, R₂=5Ω