If the total voltage is 60 volts, what is the voltage at R3?
Understand the Problem
The question asks us to determine the voltage at resistor R3 when the total voltage in a circuit is given as 60 volts. To solve this, we can use the principles of series and parallel circuits to find the voltage drop across R3.
Answer
The voltage at resistor $R_3$ is $36 V$.
Answer for screen readers
The voltage at resistor $R_3$ is $36 V$.
Steps to Solve
- 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).
- 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:
$$ \frac{1}{R_{eq}} = \frac{1}{5} + \frac{1}{20} $$
- Solve for R_eq
Calculate:
$$ \frac{1}{R_{eq}} = \frac{4}{20} + \frac{1}{20} = \frac{5}{20} = \frac{1}{4} $$
Thus,
$$ R_{eq} = 4 \Omega $$
- Find the total resistance in the circuit
Now, add $R_{eq}$ to $R_3$:
$$ R_{total} = R_{eq} + R_3 = 4 + 6 = 10 \Omega $$
- Calculate the total current in the circuit
Using Ohm’s law $V = IR$, we can find the total current $I_{total}$:
$$ I_{total} = \frac{V_{total}}{R_{total}} = \frac{60}{10} = 6 A $$
- Find the voltage drop across R3
Now, using Ohm’s law again, the voltage drop across $R_3$ is:
$$ V_{R3} = I_{total} \cdot R_3 = 6 \cdot 6 = 36 V $$
The voltage at resistor $R_3$ is $36 V$.
More Information
In this circuit, the combination of series and parallel resistors often simplifies the calculations for voltage and current. Resistors in parallel reduce the overall resistance, which affects how voltage is distributed in the circuit.
Tips
- Forgetting to calculate the equivalent resistance of parallel resistors before adding them to the series resistor.
- Not applying Ohm's law correctly, particularly confusion in using total current versus individual branch currents.