https://file.aiquickdraw.com/mathbot/file/1727316897200ekhvvcye.jpg

This is a simple circuit problem that asks to find the total current and the voltage drop across each resistor. Here's how we can approach it step-by-step:

### 1. **Determine the Total Resistance:**
   The circuit shown in the image appears to be a **series circuit**, meaning that the total resistance is simply the sum of all individual resistances.

   The given resistances are:
   - \( R_1 = 20 \, \Omega \)
   - \( R_2 = 12 \, \Omega \)
   - \( R_3 = 15.5 \, \Omega \)
   - \( R_4 = 25 \, \Omega \)

   The total resistance \( R_{total} \) is calculated as:

   \[
   R_{total} = R_1 + R_2 + R_3 + R_4
   \]

   Substituting the values:

   \[
   R_{total} = 20 + 12 + 15.5 + 25 = 72.5 \, \Omega
   \]

### 2. **Find the Total Current \( I_{total} \):**
   Using Ohm's Law, we can find the total current in the circuit. The voltage across the entire circuit is given as \( V = 220 \, \text{V} \).

   Ohm's Law is:
   \[
   I_{total} = \frac{V}{R_{total}}
   \]

   Substituting the values:

   \[
   I_{total} = \frac{220}{72.5} \approx 3.03 \, \text{A}
   \]

### 3. **Find the Voltage Drop Across Each Resistor:**
   The voltage drop across each resistor in a series circuit is calculated by Ohm’s Law:

   \[
   V_R = I_{total} \times R
   \]

   - For \( R_1 = 20 \, \Omega \):
     \[
     V_{R_1} = 3.03 \times 20 = 60.6 \, \text{V}
     \]

   - For \( R_2 = 12 \, \Omega \):
     \[
     V_{R_2} = 3.03 \times 12 = 36.36 \, \text{V}
     \]

   - For \( R_3 = 15.5 \, \Omega \):
     \[
     V_{R_3} = 3.03 \times 15.5 = 46.97 \, \text{V}
     \]

   - For \( R_4 = 25 \, \Omega \):
     \[
     V_{R_4} = 3.03 \times 25 = 75.75 \, \text{V}
     \]

### Final Answer:
- **Total current**: \( I_{total} \approx 3.03 \, \text{A} \)
- **Voltage drops**:
  - \( V_{R_1} \approx 60.6 \, \text{V} \)
  - \( V_{R_2} \approx 36.36 \, \text{V} \)
  - \( V_{R_3} \approx 46.97 \, \text{V} \)
  - \( V_{R_4} \approx 75.75 \, \text{V} \)

Would you like further details or have any other questions? Here are some related questions:

1. What is the significance of current being the same in series circuits?
2. How would the problem change if the circuit was a parallel circuit instead?
3. How is power consumption calculated in a series circuit?
4. What happens to the total resistance if more resistors are added in series?
5. Can you explain the relationship between voltage, current, and resistance?

**Tip**: In series circuits, the total voltage is the sum of the individual voltage drops across each component, and the current remains the same throughout.

Find the total current and the voltage drop of each resistance in the series circuit with R1 = 20Ω, R2 = 12Ω, R3 = 15.5Ω, R4 = 25Ω, and total voltage of 220V.

Learn how to calculate the total current and voltage drop across each resistor in a series circuit with resistances of 20Ω, 12Ω, 15.5Ω, and 25Ω, powered by a 220V source. This step-by-step solution covers Ohm's Law and circuit analysis.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation