Worksheet - Series Circuit Problems - Worksheet- Series Circuit ... - Free Printable

Let's go through each of the six series circuit problems on this worksheet and verify or solve them step by step, using Ohm’s Law and the rules for series circuits.

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🔧 Series Circuit Rules Recap:

- Current (I) is the same through all components.
- Total Voltage (Vₜ) = Sum of voltage drops across each resistor.
- Total Resistance (Rₜ) = Sum of individual resistances:
$ R_T = R_1 + R_2 + R_3 + \dots $
- Ohm’s Law: $ V = IR $ → $ I = \frac{V}{R} $, $ V = IR $

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## ✔ Problem 1:
Given:
- $ R_1 = 10\,\Omega $
- $ R_2 = 20\,\Omega $
- Battery voltage = 90 V

Step 1: Total Resistance
$$
R_T = R_1 + R_2 = 10 + 20 = 30\,\Omega
$$

Step 2: Total Current
$$
I_T = \frac{V_T}{R_T} = \frac{90\,V}{30\,\Omega} = 3\,A
$$

Step 3: Voltage Drops
- $ V_1 = I \cdot R_1 = 3\,A \cdot 10\,\Omega = 30\,V $
- $ V_2 = I \cdot R_2 = 3\,A \cdot 20\,\Omega = 60\,V $

✔ All values are correct:
- $ R_T = 30\,\Omega $
- $ I_T = 3\,A $
- $ I_1 = I_2 = 3\,A $
- $ V_1 = 30\,V $, $ V_2 = 60\,V $

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## ✔ Problem 2:
Given:
- $ R_1 = 6\,\Omega $
- $ R_2 = 14\,\Omega $
- $ R_3 = 10\,\Omega $
- Battery = 60 V

Step 1: Total Resistance
$$
R_T = 6 + 14 + 10 = 30\,\Omega
$$

Step 2: Total Current
$$
I_T = \frac{60\,V}{30\,\Omega} = 2\,A
$$

Wait! The student wrote $ I_T = 3\,A $. That’s incorrect.

Let’s recalculate:
$$
I_T = \frac{60}{30} = 2\,A
$$

Then:
- $ V_1 = 2\,A \cdot 6\,\Omega = 12\,V $
- $ V_2 = 2\,A \cdot 14\,\Omega = 28\,V $
- $ V_3 = 2\,A \cdot 10\,\Omega = 20\,V $

But student wrote:
- $ V_1 = 18\,V $, $ V_2 = 42\,V $, $ V_3 = 30\,V $ — which implies current of 3 A.

✘ So student made a mistake here.

✔ Correct answers:
- $ R_T = 30\,\Omega $
- $ I_T = 2\,A $
- $ I_1 = I_2 = I_3 = 2\,A $
- $ V_1 = 12\,V $, $ V_2 = 28\,V $, $ V_3 = 20\,V $

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## ✔ Problem 3:
Given:
- Battery = 75 V
- $ R_1 = 10\,\Omega $
- Ammeter reads 5 A → so $ I_T = 5\,A $
- Voltmeter across $ R_2 $ reads 25 V → $ V_2 = 25\,V $

Find: $ V_1 $, $ I_2 $, $ R_2 $

Since it’s a series circuit:
- $ I_T = I_1 = I_2 = 5\,A $

Voltage drop across $ R_1 $:
$$
V_1 = I \cdot R_1 = 5\,A \cdot 10\,\Omega = 50\,V
$$

Total voltage:
$$
V_T = V_1 + V_2 = 50 + 25 = 75\,V \quad \text{✓ matches battery}
$$

Now find $ R_2 $:
$$
R_2 = \frac{V_2}{I_2} = \frac{25\,V}{5\,A} = 5\,\Omega
$$

But student wrote $ R_2 = 10\,\Omega $? ✘ Incorrect.

✔ Correct:
- $ V_1 = 50\,V $
- $ I_2 = 5\,A $
- $ R_2 = 5\,\Omega $

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## ✔ Problem 4:
Given:
- $ R_1 = 5\,\Omega $
- $ R_2 = 15\,\Omega $
- Current $ I = 5\,A $
- Find $ V_1 $, $ V_2 $, $ V_T $

Step 1: Voltage Drops
- $ V_1 = I \cdot R_1 = 5\,A \cdot 5\,\Omega = 25\,V $
- $ V_2 = I \cdot R_2 = 5\,A \cdot 15\,\Omega = 75\,V $
- $ V_T = V_1 + V_2 = 25 + 75 = 100\,V $

Student wrote:
- $ V_1 = 25\,V $
- $ V_2 = 75\,V $
- $ V_T = 100\,V $

✔ All correct!

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## ✔ Problem 5:
Given:
- $ R_1 = 5\,\Omega $
- $ R_2 = 3\,\Omega $
- $ R_3 = 2\,\Omega $
- Battery = 20 V

Step 1: Total Resistance
$$
R_T = 5 + 3 + 2 = 10\,\Omega
$$

Step 2: Total Current
$$
I_T = \frac{20\,V}{10\,\Omega} = 2\,A
$$

Step 3: Voltage Drops
- $ V_1 = 2\,A \cdot 5\,\Omega = 10\,V $
- $ V_2 = 2\,A \cdot 3\,\Omega = 6\,V $
- $ V_3 = 2\,A \cdot 2\,\Omega = 4\,V $

Student wrote:
- $ R_T = 10\,\Omega $
- $ I_T = 2\,A $
- $ V_1 = 10\,V $, $ V_2 = 6\,V $, $ V_3 = 4\,V $

✔ All correct!

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## ✔ Problem 6:
Given:
- Battery = 40 V
- $ R_3 = 10\,\Omega $
- Voltmeter across $ R_3 $ shows 20 V
- Voltmeter across $ R_2 $ shows 10 V
- $ I_3 = 2\,A $ (given)

We need to find $ R_1 $, $ R_2 $, $ V_1 $

Step 1: Use $ I_3 = 2\,A $

Since series: $ I_T = I_1 = I_2 = I_3 = 2\,A $

Step 2: Check $ V_3 $

$$
V_3 = I \cdot R_3 = 2\,A \cdot 10\,\Omega = 20\,V \quad \text{✓ matches voltmeter}
$$

Step 3: $ V_2 = 10\,V $ → find $ R_2 $

$$
R_2 = \frac{V_2}{I_2} = \frac{10\,V}{2\,A} = 5\,\Omega
$$

Step 4: $ V_T = 40\,V $

So $ V_1 = V_T - V_2 - V_3 = 40 - 10 - 20 = 10\,V $

Now $ R_1 = \frac{V_1}{I_1} = \frac{10\,V}{2\,A} = 5\,\Omega $

Student wrote:
- $ I_3 = 2\,A $
- $ I_1 = 2\,A $
- $ V_1 = 10\,V $
- $ R_1 = 5\,\Omega $
- $ R_2 = 5\,\Omega $

✔ All correct!

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🟩 Summary of Corrections:

| Problem | Student Answer | Correction |
|--------|----------------|-----------|
| 1 | ✔ All correct | ✔️ |
| 2 | ✘ $ I_T = 3\,A $, voltages wrong | Should be $ I_T = 2\,A $, $ V_1=12\,V $, $ V_2=28\,V $, $ V_3=20\,V $ |
| 3 | ✘ $ R_2 = 10\,\Omega $ | Should be $ R_2 = 5\,\Omega $ |
| 4 | ✔ All correct | ✔️ |
| 5 | ✔ All correct | ✔️ |
| 6 | ✔ All correct | ✔️ |

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✔ Final Answers (Corrected):

#### Problem 2:
- $ R_T = 30\,\Omega $
- $ I_T = 2\,A $
- $ I_1 = I_2 = I_3 = 2\,A $
- $ V_1 = 12\,V $, $ V_2 = 28\,V $, $ V_3 = 20\,V $

#### Problem 3:
- $ V_1 = 50\,V $
- $ I_2 = 5\,A $
- $ R_2 = 5\,\Omega $

All others are correct as written.

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Let me know if you’d like a cleaned-up version of the worksheet with corrections!