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This circuit appears to show two voltage sources \( E_1 \) and \( E_2 \), a resistor \( R \), and a potential difference \( U_{ab} \) between points \( a \) and \( b \). The goal is to calculate the current \( I \) through the resistor \( R \).

### Given dataThis circuit appears to show two voltage sources \( E_1 \) and \( E_2 \), a resistor \( R \), and a potential difference \( U_{ab} \) between points \( a \) and \( b \). The goal is to calculate the current \( I \) through the resistor \( R \).

### Given 
- \( U_{ab} = 100 \, \text{V} \) (potential difference between points \( a \) and \( b \)),
- \( E_1 = 20 \, \text{V} \) (voltage source 1),
- \( E_2 = 50 \, \text{V} \) (voltage source 2),
- \( R = 10 \, \Omega \) (resistor value),
- We need to find the current \( I \).

### Approach:

Using Kirchhoff's Voltage Law (KVL), we can write the equation for the total voltage in the loop. From the diagram, we assume the following:

1. The current flows clockwise, starting from point \( a \) to \( b \) through the resistor.
2. The potential difference \( U_{ab} \) is given as \( 100 \, \text{V} \).
3. The voltage drops across \( E_1 \) and \( E_2 \) need to be considered.

#### KVL Equation:
\[
U_{ab} = E_1 + E_2 + I \cdot R
\]
Now, let's solve for the current \( I \):

\[
I = \frac{U_{ab} - (E_1 + E_2)}{R}
\]

### Substituting the values:
\[
I = \frac{100 \, \text{V} - (20 \, \text{V} + 50 \, \text{V})}{10 \, \Omega}
\]
\[
I = \frac{100 \, \text{V} - 70 \, \text{V}}{10 \, \Omega}
\]
\[
I = \frac{30 \, \text{V}}{10 \, \Omega} = 3 \, \text{A}
\]

Thus, the current \( I \) is **3 A**.

Would you like a detailed breakdown of each step or further clarification?

Here are 5 related questions:
1. How does Kirchhoff's Voltage Law apply to different circuits?
2. What happens to the current if one of the voltage sources is reversed?
3. How does changing the resistance \( R \) affect the current in the circuit?
4. How can we determine the power dissipated by the resistor \( R \)?
5. How would the result change if the voltage difference \( U_{ab} \) was smaller?

**Tip**: In circuits with multiple sources, always check the direction of each source when applying Kirchhoff's Laws to avoid sign errors.

Задача 1: Calculate the current I in the circuit given Uab = 100 V, E1 = 20 V, E2 = 50 V, and R = 10 Ω.

Learn how to calculate the current in a circuit with two voltage sources (E1 = 20 V, E2 = 50 V) and a resistor (R = 10 Ω) using Kirchhoff's Voltage Law and Ohm's Law. Given Uab = 100 V, solve for the current I. Suitable for advanced high school or college-level physics.

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