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The problem you've provided is about a series circuit where resistances \( R_1 \), \( R_2 \), and \( R_3 \) are given, and the goal is to find:

1. The total resistance (\( R_S \)) of the circuit.
2. The total current (\( I_S \)) in the circuit.

Here’s the information given:

- \( R_1 = 2 \, \Omega \)
- \( R_2 = 2 \times R_1 = 2 \times 2 = 4 \, \Omega \)
- \( R_3 = \frac{1}{2} \times R_2 = \frac{1}{2} \times 4 = 2 \, \Omega \)
- \( V = 12 \, V \) (total voltage)

### a) Finding the total resistance \( R_S \):
Since all the resistors are connected in series, the total resistance \( R_S \) is the sum of the individual resistances:
\[
R_S = R_1 + R_2 + R_3 = 2 + 4 + 2 = 8 \, \Omega
\]

### b) Finding the total current \( I_S \):
Using Ohm's Law, the total current \( I_S \) in a series circuit can be calculated as:
\[
I_S = \frac{V}{R_S} = \frac{12 \, V}{8 \, \Omega} = 1.5 \, A
\]

### Final Answers:
- \( R_S = 8 \, \Omega \)
- \( I_S = 1.5 \, A \)

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:
1. What is the voltage drop across each resistor in this series circuit?
2. How would the total resistance change if \( R_2 \) was instead parallel with \( R_3 \)?
3. What is the power dissipated by each resistor?
4. How does the total current compare if the voltage is doubled while keeping the resistances the same?
5. How would the total current change if \( R_1 \) was replaced with a 1 \( \Omega \) resistor?

**Tip:** In a series circuit, the current remains the same through all components, but the voltage drop across each resistor varies depending on its resistance.

A circuit with three resistors (R1, R2, R3) connected in series, with given resistances. Find the total resistance (Rs) and the total current (Is) in the circuit. Known values are: R1 = 2 Ω, R2 = 2 * R1, R3 = 1/2 * R2, and V = 12V.

Solve for the total resistance and current in a series circuit with resistors R1, R2, and R3. Using Ohm's Law, the solution explains key formulas and steps, with R1 = 2 Ω, R2 = 2 * R1, R3 = 1/2 * R2, and V = 12V.

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