Questions: Find the current flowing across the 20 Ω resistor.

Solution Steps

The 35 Ω and 20 Ω resistors are connected in series. Their equivalent resistance is: R_series = 35 Ω + 20 Ω = 55 Ω

The equivalent series resistance (55 Ω) is in parallel with the 15 Ω resistor. The total equivalent resistance is calculated as follows:

1/R_total = 1/55 Ω + 1/15 Ω 1/R_total = (15 + 55) / (55 * 15) Ω⁻¹ 1/R_total = 70 / 825 Ω⁻¹ R_total = 825 / 70 Ω R_total ≈ 11.79 Ω

Using Ohm's law (V = IR), the total current flowing through the circuit is: I_total = V / R_total I_total = 10 V / 11.79 Ω I_total ≈ 0.85 A

The voltage across the series combination of the 35 Ω and 20 Ω resistors is the same as the voltage across the 15 Ω resistor (since they're in parallel) and equal to the source voltage: 10V

Since the 35 Ω and 20 Ω resistors are in series, the current flowing through them is the same. Using Ohm's law:

I_20Ω = V_series / R_series I_20Ω = 10 V / 55 Ω I_20Ω ≈ 0.18 A

Final Answer