Question
A 20 A circuit has a design current of 18 A and voltage drop of 19.5 \( \mathrm{mV} / \mathrm{A} / \mathrm{m} \). If its circuit length is 25 m, what is the overall voltage drop ?
Ask by Dunn Ramos. in Singapore
Jan 20,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The overall voltage drop is approximately **8.78 V**.
Solution
To calculate the overall voltage drop in the circuit, you can use the following formula:
\[
V_{\text{drop}} = (\text{Voltage drop per A per m}) \times \text{Current} \times \text{Length}
\]
**Given:**
- Voltage drop per A per m = 19.5 mV/A/m
- Current = 18 A
- Length = 25 m
**Step-by-Step Calculation:**
1. **Convert millivolts to volts:**
\[
19.5 \, \text{mV/A/m} = 19.5 \times 10^{-3} \, \text{V/A/m}
\]
2. **Multiply by current and length:**
\[
V_{\text{drop}} = 19.5 \times 10^{-3} \, \text{V/A/m} \times 18 \, \text{A} \times 25 \, \text{m}
\]
3. **Calculate the numerical value:**
\[
19.5 \times 18 = 351
\]
\[
351 \times 25 = 8775
\]
\[
8775 \times 10^{-3} = 8.775 \, \text{V}
\]
4. **Round to two decimal places:**
\[
V_{\text{drop}} \approx 8.78 \, \text{V}
\]
**Final Answer:**
The overall voltage drop is approximately **8.78 V**.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To find the overall voltage drop in the circuit, you can use the formula: \[ \text{Voltage Drop} = \text{Current (I)} \times \text{Voltage Drop per unit length} \times \text{Length (L)} \] Given: - Current (I) = 20 A - Voltage Drop per unit length = 19.5 mV/A/m = 0.0195 V/A/m - Length (L) = 25 m Now plug in the values: \[ \text{Voltage Drop} = 20 \, \text{A} \times 0.0195 \, \text{V/A/m} \times 25 \, \text{m} \] Calculating this gives: \[ \text{Voltage Drop} = 20 \times 0.0195 \times 25 = 9.75 \, \text{V} \] So, the overall voltage drop in the circuit is 9.75 V.
