Question

The current in the circuit shown is 2.0 A.

A diagram of a closed circuit with a power source on the left labeled 30 V. There are 3 resistors in series, connected to it labeled 2 Ohms, 3 Ohms and R Subscript 3 baseline.
What is the value of R3?

10 Ω
15 Ω
20 Ω
55 Ω

Answer 1

To find the value of the resistor \( R_3 \) in the circuit, we can use Ohm's Law and the fact that the resistors are in series.

1. **Total Voltage** (V): The power source provides 30 V.

2. **Total Current** (I): The current through the circuit is given as 2.0 A.

3. **Total Resistance** (R_total): According to Ohm's Law, \( V = I \cdot R_{total} \).
\[
R_{total} = \frac{V}{I} = \frac{30 \text{ V}}{2.0 \text{ A}} = 15 \, \text{Ω}
\]

4. **Resistance of Resistors in Series**: For resistors in series, the total resistance is the sum of the individual resistances:
\[
R_{total} = R_1 + R_2 + R_3
\]
where \( R_1 = 2 \, \Omega \) and \( R_2 = 3 \, \Omega \).

So we have:
\[
15 \, \Omega = 2 \, \Omega + 3 \, \Omega + R_3
\]

5. **Solve for \( R_3 \)**:
\[
15 \, \Omega = 5 \, \Omega + R_3
\]
\[
R_3 = 15 \, \Omega - 5 \, \Omega = 10 \, \Omega
\]

Thus, the value of \( R_3 \) is **10 Ω**.