Calculate the equivalent inductance of the circuit below, in mH. Inductors one through three have size 13.8 mH, and inductors four through five have inductance 8.6 mH. L1 L2 L3 L4 L5
Calculate the equivalent inductance of the circuit below, in mH. Inductors one through three have size 13.8 mH, and inductors four through five have inductance 8.6 mH. L1 L2 L3 L4 L5
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(Please answer to the fourth decimal place - i.e 14.3225)
![**Calculate the Equivalent Inductance of the Given Circuit**
**Problem Statement:**
Calculate the equivalent inductance of the circuit below, in mH. Inductors one through three have size 13.8 mH, and inductors four through five have inductance 8.6 mH.
**Circuit Diagram Explanation:**
The given image shows a circuit diagram with five inductors: L1, L2, L3, L4, and L5, configured in a combination of series and parallel connections.
- **Inductors L1, L2, and L3** are connected in parallel.
- **Inductors L4 and L5** are connected in parallel.
- The parallel combinations of L1, L2, and L3, and L4, L5 are connected in series with each other.
**Inductance Values:**
- \( L1 = L2 = L3 = 13.8 \text{ mH} \)
- \( L4 = L5 = 8.6 \text{ mH} \)
**Step-by-Step Solution:**
1. **Calculate the equivalent inductance of the parallel combination of L1, L2, and L3:**
\[ \frac{1}{L_{123}} = \frac{1}{L1} + \frac{1}{L2} + \frac{1}{L3} \]
Given \( L1 = L2 = L3 = 13.8 \text{ mH} \):
\[ \frac{1}{L_{123}} = \frac{1}{13.8 \text{ mH}} + \frac{1}{13.8 \text{ mH}} + \frac{1}{13.8 \text{ mH}} \]
\[ \frac{1}{L_{123}} = \frac{3}{13.8} \]
\[ L_{123} = \frac{13.8}{3} \]
\[ L_{123} = 4.6 \text{ mH} \]
2. **Calculate the equivalent inductance of the parallel combination of L4 and L5:**
\[ \frac{1}{L_{45}} = \frac{1}{L4} + \frac{1}{L5} \]
Given \( L4 = L5 = 8.6 \text{ mH} \):
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Transcribed Image Text:**Calculate the Equivalent Inductance of the Given Circuit**
**Problem Statement:**
Calculate the equivalent inductance of the circuit below, in mH. Inductors one through three have size 13.8 mH, and inductors four through five have inductance 8.6 mH.
**Circuit Diagram Explanation:**
The given image shows a circuit diagram with five inductors: L1, L2, L3, L4, and L5, configured in a combination of series and parallel connections.
- **Inductors L1, L2, and L3** are connected in parallel.
- **Inductors L4 and L5** are connected in parallel.
- The parallel combinations of L1, L2, and L3, and L4, L5 are connected in series with each other.
**Inductance Values:**
- \( L1 = L2 = L3 = 13.8 \text{ mH} \)
- \( L4 = L5 = 8.6 \text{ mH} \)
**Step-by-Step Solution:**
1. **Calculate the equivalent inductance of the parallel combination of L1, L2, and L3:**
\[ \frac{1}{L_{123}} = \frac{1}{L1} + \frac{1}{L2} + \frac{1}{L3} \]
Given \( L1 = L2 = L3 = 13.8 \text{ mH} \):
\[ \frac{1}{L_{123}} = \frac{1}{13.8 \text{ mH}} + \frac{1}{13.8 \text{ mH}} + \frac{1}{13.8 \text{ mH}} \]
\[ \frac{1}{L_{123}} = \frac{3}{13.8} \]
\[ L_{123} = \frac{13.8}{3} \]
\[ L_{123} = 4.6 \text{ mH} \]
2. **Calculate the equivalent inductance of the parallel combination of L4 and L5:**
\[ \frac{1}{L_{45}} = \frac{1}{L4} + \frac{1}{L5} \]
Given \( L4 = L5 = 8.6 \text{ mH} \):
\[ \
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