https://file.aiquickdraw.com/mathbot/file/1726921479407b9e0br7w.jpg

The image shows an electrical circuit problem. Here is the important information:

1. Three electromotive forces (EMF) are given:
   - \( \varepsilon_1 = 3 \, \text{V} \)
   - \( \varepsilon_2 = 12 \, \text{V} \)
   - \( \varepsilon_3 = 3 \, \text{V} \)

2. The resistances in the circuit are:
   - \( R_1 = 1 \, \Omega \)
   - \( R_2 = 2 \, \Omega \)
   - \( R_3 = 2 \, \Omega \)

The problem asks to find the electric current (\( I \)) flowing through the circuit.

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### To solve this, we can apply **Kirchhoff's Laws**:

1. **First step:** Apply **Kirchhoff's Voltage Law (KVL)** to the loop. The sum of the voltages in a closed loop must equal zero.

\[
\varepsilon_1 + \varepsilon_2 + \varepsilon_3 = I \cdot (R_1 + R_2 + R_3)
\]

Let's solve this system step by step:

\[
(3 \, \text{V}) + (12 \, \text{V}) + (3 \, \text{V}) = I \cdot (1 \, \Omega + 2 \, \Omega + 2 \, \Omega)
\]

\[
18 \, \text{V} = I \cdot 5 \, \Omega
\]

2. **Second step:** Solve for \( I \):

\[
I = \frac{18 \, \text{V}}{5 \, \Omega} = 3.6 \, \text{A}
\]

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### The current flowing in the circuit is \( 3.6 \, \text{A} \).

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Would you like further details on the method or other parts of the question?

### Here are 5 related questions to expand understanding:

1. How would the current change if one of the resistors increased?
2. What happens if the direction of one of the voltage sources is reversed?
3. Can you apply Ohm's Law to determine the voltage drop across each resistor?
4. How do Kirchhoff's Current and Voltage Laws apply to more complex circuits?
5. How do you calculate the power dissipated by each resistor?

**Tip:** Kirchhoff's Voltage Law is useful for analyzing any closed loop within a circuit, ensuring energy conservation in electrical systems.

Given a circuit with three electromotive forces and three resistances, calculate the current flowing through the circuit. The given values are: ε1 = 3V, ε2 = 12V, ε3 = 3V, R1 = 1Ω, R2 = 2Ω, R3 = 2Ω.

Learn how to calculate the current flowing through a circuit using Kirchhoff's Voltage Law and Ohm's Law. This problem involves three electromotive forces and three resistors, with step-by-step calculations for finding the total current.

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