Applying Conservation of Charge to Junctions in Circuits

Q: What are the magnitudes and directions of the currents $I_B$ and $I_C$ in segments B and C?

Background

Topic: Conservation of Charge in Electric Circuits

This question tests your understanding of how electric current splits and combines at junctions in a circuit, using the principle that charge is conserved (Kirchhoff's Current Law).

Key Terms and Formulas:

• Current ($I$): The flow of electric charge, measured in amperes (A).

• Kirchhoff's Current Law (KCL): The total current entering a junction equals the total current leaving the junction.

• Junction Equation: $\sum I_{\text{in}} = \sum I_{\text{out}}$

Step-by-Step Guidance

1. Identify all currents entering and leaving each junction. Label unknown currents as $i_1$, $i_2$, $I_B$, and $I_C$ as shown in the second diagram.

2. Write a junction equation for the first junction (where 5 A enters and splits into 3 A and $i_1$): $5\,\text{A} = 3\,\text{A} + i_1$

3. Write a junction equation for the second junction (where $i_1$ splits into 1 A and $I_B$): $i_1 = 1\,\text{A} + I_B$

4. Write a junction equation for the third junction (where 3 A splits into $i_2$ and 2 A): $3\,\text{A} = i_2 + 2\,\text{A}$

5. Write a junction equation for the fourth junction (where $i_2$ and $I_B$ combine to form $I_C$): $i_2 + I_B = I_C$

Try solving on your own before revealing the answer!

Final Answer:

$I_B = 1\,\text{A}$ to the right, $I_C = 2\,\text{A}$ to the right.

By applying the junction equations and conservation of charge, you find the values for $I_B$ and $I_C$.