Question

Find the current through the 10Ω resistor shown in the figure.

Hint:

To find the current in a circuit, always apply Kirchhoff’s Laws and Ohm’s Law. Simplify the circuit step by step if necessary.

Answer 1

Step 1: Apply Kirchhoff’s Rules.
We are given a circuit with resistors of \( 10 \, \Omega \), \( 3 \, \Omega \), and \( 6 \, \Omega \), and a voltage source of \( 3 \, \text{V} \) and \( 5 \, \text{V} \). We will apply Kirchhoff’s Voltage Law (KVL) to the loop and solve for the current using Ohm’s Law: \[ I = \frac{V_{\text{total}}}{R_{\text{total}}} \] Where \( V_{\text{total}} = 3 \, \text{V} + 5 \, \text{V} \) and \( R_{\text{total}} = 10 \, \Omega + 3 \, \Omega + 6 \, \Omega \).
After solving the equation, we get: \[ I = \frac{8}{19} \approx 0.42 \, \text{A} \]
Final Answer:
The current through the 10Ω resistor is \( \boxed{0.42 \, \text{A}} \).