If the total voltage is 60 volts, what is the voltage at R3?

Steps to Solve

1. Identify the circuit configuration

This circuit has a combination of series and parallel resistors. Resistor $R_1$ (5Ω) and resistor $R_2$ (20Ω) are in parallel, and their combined resistance is in series with $R_3$ (6Ω).

2. Calculate the equivalent resistance of R1 and R2

To find the equivalent resistance of the parallel resistors, use the formula:

$$ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} $$

Substituting the values:

$$ \frac{1}{R_{eq}} = \frac{1}{5} + \frac{1}{20} $$

3. Solve for R_eq

Calculate:

$$ \frac{1}{R_{eq}} = \frac{4}{20} + \frac{1}{20} = \frac{5}{20} = \frac{1}{4} $$

Thus,

$$ R_{eq} = 4 \Omega $$

4. Find the total resistance in the circuit

Now, add $R_{eq}$ to $R_3$:

$$ R_{total} = R_{eq} + R_3 = 4 + 6 = 10 \Omega $$

5. Calculate the total current in the circuit

Using Ohm’s law $V = IR$, we can find the total current $I_{total}$:

$$ I_{total} = \frac{V_{total}}{R_{total}} = \frac{60}{10} = 6 A $$

6. Find the voltage drop across R3

Now, using Ohm’s law again, the voltage drop across $R_3$ is:

$$ V_{R3} = I_{total} \cdot R_3 = 6 \cdot 6 = 36 V $$