Solved Series Circuit Worksheet #3 E=12 volts II=1 amperes | Chegg.com - Free Printable

Let's solve each problem on the Series Circuit Worksheet #3 step by step using Ohm’s Law and the principles of series circuits.

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🔧 Key Concepts for Series Circuits:

1. Total Resistance (Rₜ):
$$
R_T = R_1 + R_2 + R_3 + \dots
$$

2. Current (I):
- Same everywhere in a series circuit.
- $ I_T = I_1 = I_2 = \dots $

3. Voltage (E):
- Total voltage is the sum of voltage drops across resistors.
- $ E = I_T \times R_T $
- Or, $ E = V_1 + V_2 + V_3 + \dots $

4. Ohm’s Law:
$$
E = I \times R \quad \Rightarrow \quad I = \frac{E}{R}, \quad R = \frac{E}{I}
$$

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Now let's go through each question:

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Problem 1:

Given:
- $ E = 12 $ volts
- $ I_T = 6 $ amperes
- $ R_1 = 1\ \Omega $
- $ R_2 = 1\ \Omega $
- $ R_3 = 1\ \Omega $
- $ R_4 = 1\ \Omega $

Find: Missing value?
Wait — all resistors are given, but nothing is labeled as unknown. Let's check what's missing.

Actually, looking at the diagram and text, it seems like we’re to find something, but the blank is not labeled. But from the context, likely we need to verify or calculate total resistance or check consistency.

But wait — perhaps there’s a typo or formatting issue. Looking closely:

> E = 12
> I_T = 6 amperes
> R1 = 1 ohm, R2 = 1 ohm, R3 = 1 ohm, R4 = 1 ohm

So total resistance:
$$
R_T = 1+1+1+1 = 4\ \Omega
$$

Then, expected current:
$$
I = \frac{E}{R_T} = \frac{12}{4} = 3\ \text{amperes}
$$

But it says $ I_T = 6 $ amperes → Contradiction!

This means either:
- The values are inconsistent, or
- We're supposed to find a missing resistor?

Wait — maybe one of the resistors is missing? No, all four are listed.

Wait — perhaps one of the values is missing, and we're to compute it?

But in this case, all resistances are given, so unless the problem is to find E or I, but both are given.

Hmm. Perhaps the question is to verify or find something else?

Wait — look at the format: It says "E = 12", "I_T = 6", then lists resistors.

But with 4 × 1Ω = 4Ω, current should be 3A, not 6A.

So either the values are wrong, or we are to find a missing value.

But no blank is shown.

Wait — perhaps the blank is under "E =", but it says "E = 12" — already filled.

Alternatively, maybe this is a trick question to show inconsistency?

But that doesn't make sense.

Wait — let's look at Problem 2 — same pattern.

Maybe the blank is in the diagram?

Looking carefully at the image:

In Problem 1, below the diagram, it says:

> E = 12
> I_T = 6 amperes
> R1 = 1 ohm
> R2 = 1 ohm
> R3 = 1 ohm
> R4 = 1 ohm

No blank. So perhaps this one is just for practice? Or maybe the goal is to calculate total resistance?

But the worksheet has blanks in others.

Wait — perhaps in Problem 1, the value of E is missing? But it says E = 12.

Wait — actually, looking more carefully, the first line says "E = ___", but in your image, it's written as "E = 12".

Possibly you've typed it incorrectly.

But in the original image, it appears that E is given as 12, I_T = 6, and all resistors are given.

So this is inconsistent because:

- $ R_T = 4\ \Omega $
- $ I_T = 6\ A $
- Then $ E = I_T \times R_T = 6 \times 4 = 24\ V $

But E is given as 12V → contradiction.

So either:
- E should be 24V, or
- I_T should be 3A, or
- One resistor is different.

But since all resistors are 1Ω, and E=12V, then I must be 3A.

So likely, the value of I_T is incorrect or E is incorrect.

But since it's a worksheet, probably the intention is to use Ohm’s Law to find a missing value.

But here, no blank is visible.

Wait — perhaps Problem 1 is to find the total resistance?

But it's clearly 4Ω.

Alternatively, maybe the blank is under "I_T", but it says 6A.

Wait — let's move to Problem 2 — maybe it's clearer.

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Problem 2:

Given:
- $ I_T = 3 $ amperes
- $ R1 = 0.5\ \Omega $
- $ R2 = 1\ \Omega $
- $ R3 = 0.5\ \Omega $
- $ R4 = 1\ \Omega $
- $ E = ? $

We are to find E.

Total resistance:
$$
R_T = R1 + R2 + R3 + R4 = 0.5 + 1 + 0.5 + 1 = 3\ \Omega
$$

Current: $ I_T = 3\ A $

So:
$$
E = I_T \times R_T = 3 \times 3 = 9\ \text{volts}
$$

✔ So E = 9 volts

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Problem 3:

Given:
- $ E = 4 $ volts
- $ I_T = ? $
- $ R_T = 3\ \Omega $

We are to find $ I_T $

Using Ohm’s Law:
$$
I_T = \frac{E}{R_T} = \frac{4}{3} \approx 1.333\ \text{amperes}
$$

So $ I_T = \frac{4}{3} $ or $ 1.\overline{3} $ A

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Problem 4:

Given:
- $ E = 12 $ volts
- $ I_T = 1 $ ampere
- $ R1 = 2\ \Omega $
- $ R2 = ? $
- $ R3 = 4\ \Omega $
- $ R4 = 3\ \Omega $
- $ R5 = 1\ \Omega $

We are to find $ R2 $

First, total resistance:
$$
R_T = R1 + R2 + R3 + R4 + R5 = 2 + R2 + 4 + 3 + 1 = 10 + R2
$$

From Ohm’s Law:
$$
R_T = \frac{E}{I_T} = \frac{12}{1} = 12\ \Omega
$$

So:
$$
10 + R2 = 12 \Rightarrow R2 = 2\ \Omega
$$

✔ So R2 = 2 ohms

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Problem 5:

Given:
- $ E = 24 $ volts
- $ I_T = 12 $ amperes
- $ R1 = 0.5\ \Omega $
- $ R2 = 0.5\ \Omega $
- $ R3 = ? $
- $ R4 = 0.3\ \Omega $
- $ R5 = 0.25\ \Omega $

We are to find $ R3 $

Total resistance:
$$
R_T = \frac{E}{I_T} = \frac{24}{12} = 2\ \Omega
$$

Sum of known resistors:
$$
R1 + R2 + R4 + R5 = 0.5 + 0.5 + 0.3 + 0.25 = 1.55\ \Omega
$$

So:
$$
R3 = R_T - 1.55 = 2 - 1.55 = 0.45\ \Omega
$$

✔ So R3 = 0.45 ohms

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Problem 6:

Given:
- $ E = 24 $ volts
- $ I_T = 3 $ amperes
- $ R1 = 2\ \Omega $
- $ R2 = 1\ \Omega $
- $ R3 = 2\ \Omega $
- $ R4 = ? $
- $ R5 = 2\ \Omega $

Find $ R4 $

Total resistance:
$$
R_T = \frac{E}{I_T} = \frac{24}{3} = 8\ \Omega
$$

Sum of known resistors:
$$
R1 + R2 + R3 + R5 = 2 + 1 + 2 + 2 = 7\ \Omega
$$

So:
$$
R4 = R_T - 7 = 8 - 7 = 1\ \Omega
$$

✔ So R4 = 1 ohm

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | Inconsistent data: