College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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![### Electric Currents in Conductors
#### The diagram below shows electric currents in conductors that meet at junction P:
[**Diagram Explanation:**]
- The diagram shows four conductors meeting at a point labeled P.
- Current of magnitude 3A is flowing into junction P from the left.
- Current of magnitude 4A is flowing into junction P from the bottom.
- Current of magnitude 2A is flowing away from junction P upwards.
- There is a conductor labeled PQ, with an unknown current flowing away from junction P towards Q.
#### Question:
**What are the magnitude and direction of the current in conductor PQ?**
To find the current in conductor PQ, we make use of Kirchhoff's Current Law (KCL), which states that the total current entering a junction must equal the total current leaving the junction.
**Step-by-step Solution:**
1. **Identify Inward Currents:**
- Current flowing into P from the left: \( I_1 = 3A \)
- Current flowing into P from the bottom: \( I_2 = 4A \)
2. **Identify Outward Currents:**
- Current flowing out of P upwards: \( I_3 = 2A \)
- Current flowing out of P to the right towards Q: \( I_{PQ} \) (unknown)
3. **Apply Kirchhoff’s Current Law (KCL):**
\[
I_{in} = I_{out}
\]
\[
I_1 + I_2 = I_3 + I_{PQ}
\]
Substitute the known values:
\[
3A + 4A = 2A + I_{PQ}
\]
4. **Solve for \( I_{PQ} \):**
\[
7A = 2A + I_{PQ}
\]
\[
I_{PQ} = 5A
\]
**Conclusion:**
- The magnitude of the current in conductor PQ is 5A.
- The direction of the current is away from junction P towards Q.](https://content.bartleby.com/qna-images/question/dff7b543-7c53-4567-b2e2-82ba64a4a215/232bd319-6d8a-48a5-afce-1d2666e5f112/ogombni.jpeg)
Transcribed Image Text:### Electric Currents in Conductors
#### The diagram below shows electric currents in conductors that meet at junction P:
[**Diagram Explanation:**]
- The diagram shows four conductors meeting at a point labeled P.
- Current of magnitude 3A is flowing into junction P from the left.
- Current of magnitude 4A is flowing into junction P from the bottom.
- Current of magnitude 2A is flowing away from junction P upwards.
- There is a conductor labeled PQ, with an unknown current flowing away from junction P towards Q.
#### Question:
**What are the magnitude and direction of the current in conductor PQ?**
To find the current in conductor PQ, we make use of Kirchhoff's Current Law (KCL), which states that the total current entering a junction must equal the total current leaving the junction.
**Step-by-step Solution:**
1. **Identify Inward Currents:**
- Current flowing into P from the left: \( I_1 = 3A \)
- Current flowing into P from the bottom: \( I_2 = 4A \)
2. **Identify Outward Currents:**
- Current flowing out of P upwards: \( I_3 = 2A \)
- Current flowing out of P to the right towards Q: \( I_{PQ} \) (unknown)
3. **Apply Kirchhoff’s Current Law (KCL):**
\[
I_{in} = I_{out}
\]
\[
I_1 + I_2 = I_3 + I_{PQ}
\]
Substitute the known values:
\[
3A + 4A = 2A + I_{PQ}
\]
4. **Solve for \( I_{PQ} \):**
\[
7A = 2A + I_{PQ}
\]
\[
I_{PQ} = 5A
\]
**Conclusion:**
- The magnitude of the current in conductor PQ is 5A.
- The direction of the current is away from junction P towards Q.
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