Applying Conservation of Charge to Junctions in a Circuit

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 sum of currents entering a junction equals the sum of currents leaving the junction.

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

Step-by-Step Guidance

1. Identify all the currents and their directions at each junction. Use the labeled diagram to help visualize the flow.

2. Apply Kirchhoff's Current Law at the first junction: $5\,\text{A}$ splits into $3\,\text{A}$ and another branch. Set up the equation for the unknown current $i_1$:

   $5\,\text{A} = 3\,\text{A} + i_1$

3. At the next junction, $i_1$ splits into $1\,\text{A}$ (segment B) and another branch. Set up the equation:

   $i_1 = 1\,\text{A} + i_B$

4. Continue to the lower branch: $3\,\text{A}$ splits into $i_2$ and $2\,\text{A}$. Set up the equation:

   $3\,\text{A} = i_2 + 2\,\text{A}$

5. At the final junction, $i_2$ and $1\,\text{A}$ combine to form $i_C$. Set up the equation:

   $i_C = i_2 + 1\,\text{A}$

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 Kirchhoff's Current Law at each junction, you find the values and directions for the unknown currents.