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This image shows a simple electrical circuit with three resistors connected in series: \( R_1 = 2 \, \Omega \), \( R_2 = 1 \, \Omega \), and \( R_3 = 5 \, \Omega \). The circuit is powered by a \( 20 \, \text{V} \) voltage source.

### Steps to solve for the current \( I \) and the voltages \( V_1 \), \( V_2 \), and \( V_3 \):

1. **Total Resistance ( \( R_T \) ):**
   Since the resistors are in series, the total resistance is the sum of the individual resistances:
   \[
   R_T = R_1 + R_2 + R_3 = 2 \, \Omega + 1 \, \Omega + 5 \, \Omega = 8 \, \Omega
   \]

2. **Current ( \( I \) ):**
   The current in a series circuit is the same throughout the circuit and can be calculated using Ohm's Law:
   \[
   I = \frac{E}{R_T} = \frac{20 \, \text{V}}{8 \, \Omega} = 2.5 \, \text{A}
   \]

3. **Voltage Drops Across Each Resistor:**

   - **For \( R_1 \):**
     \[
     V_1 = I \times R_1 = 2.5 \, \text{A} \times 2 \, \Omega = 5 \, \text{V}
     \]

   - **For \( R_2 \):**
     \[
     V_2 = I \times R_2 = 2.5 \, \text{A} \times 1 \, \Omega = 2.5 \, \text{V}
     \]

   - **For \( R_3 \):**
     \[
     V_3 = I \times R_3 = 2.5 \, \text{A} \times 5 \, \Omega = 12.5 \, \text{V}
     \]

These are the key values for the circuit:
- **Total Current \( I = 2.5 \, \text{A} \)**
- **Voltage across \( R_1 (V_1) = 5 \, \text{V} \)**
- **Voltage across \( R_2 (V_2) = 2.5 \, \text{V} \)**
- **Voltage across \( R_3 (V_3) = 12.5 \, \text{V} \)**

Would you like further details on any of these calculations?

### Additional Questions:
1. What would happen if one of the resistors was removed from the circuit?
2. How does increasing the voltage source affect the current?
3. Can this circuit be simplified further if any components were parallel?
4. How would the power dissipated by each resistor be calculated?
5. What is the total power consumed by the circuit?

#### Tip:
Always check that the sum of the voltage drops across individual resistors equals the total voltage provided by the source!

Determine the total current and voltage drops across each resistor for a series circuit with resistors R1 = 2Ω, R2 = 1Ω, and R3 = 5Ω connected to a 20V source.

Learn how to solve for the total current and voltage drops across each resistor in a series circuit with resistors R1 = 2Ω, R2 = 1Ω, and R3 = 5Ω connected to a 20V source. This problem covers Ohm's Law and series circuit calculations. Suitable for students in Grades 9-12.

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