https://file.aiquickdraw.com/mathbot/file/17247020579574e3fugz4.jpg

To calculate the current in the circuit, let's analyze the given image, which shows a circuit with various components.

### Components in the Circuit:
- A 90 V voltage source in series with a 2 Ω resistor.
- A 1 Ω resistor in parallel with the combination of a 5 Ω resistor and a 45 A current source.
- A 4 Ω resistor connected in series with a 180 V voltage source.

### Analysis:
1. **Identify Loops and Nodes:**
   - We can see two loops: one on the left side with the 90 V source, the 2 Ω resistor, and the parallel combination of resistors and the current source. The other loop is on the right with the 180 V source and the 4 Ω resistor.

2. **Apply Kirchhoff's Voltage Law (KVL):**
   - **For the Left Loop:**
     \[
     90V - I_1 \cdot 2\Omega - I_1 \cdot 1\Omega = 0
     \]
     \[
     90V = I_1 \cdot 3\Omega
     \]
     \[
     I_1 = \frac{90V}{3\Omega} = 30A
     \]
   - **For the Right Loop:**
     \[
     180V - I_2 \cdot 4\Omega = 0
     \]
     \[
     I_2 = \frac{180V}{4\Omega} = 45A
     \]

3. **Total Current in the Circuit:**
   - The current source in the middle branch forces a current of 45 A through the 5 Ω resistor, and this will influence the current division between the branches.

### Solution:
- \( I_1 = 30A \) in the left loop.
- \( I_2 = 45A \) in the right loop.

Since the middle branch current is fixed by the current source to be 45 A, it overrides any current calculated by KVL/KCL in that loop. Therefore, the total current through that part of the circuit is directly influenced by the 45 A current source.

### Conclusion:
The primary current in the circuit is **45 A**, primarily dictated by the current source. The other currents (30 A) influence only the left loop but do not add up to alter the current enforced by the 45 A current source.

Would you like further clarification on any specific part of this circuit analysis or additional questions to expand your understanding?

Here are five related questions:
1. How would the circuit behave if the current source was removed?
2. What would happen if the 1 Ω resistor was shorted?
3. How do you apply mesh analysis in circuits with multiple loops?
4. What is the effect of the 45 A current source on the overall circuit current?
5. How would the current distribution change if the 90 V source were replaced with a different value?

**Tip:** In circuits with current sources, always account for the current source's direct influence on the circuit as it dictates the current in its branch.

Learn how to calculate current in a complex circuit with 90V and 180V voltage sources using Kirchhoff's Voltage Law and current source principles. Detailed analysis covers the influence of current sources on circuit behavior.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation