Question: LEARNING OBJECTIVE: Calculate the voltage of a circuit given the current and resistance.
If the current in a circuit is $3 + j2$ amps and the resistance is $4 - j3$ ohms, what is the voltage?
a.) $6 + j$ volts
b.) $18 - j$ volts
c.) $6 - j$ volts
d.) $18 + j$ volts
1. **State the problem:** We need to find the voltage $V$ in a circuit given the current $I = 3 + j2$ amps and the resistance $R = 4 - j3$ ohms.
2. **Formula used:** Voltage in a circuit is given by Ohm's Law:
$$V = I \times R$$
where $V$ is voltage, $I$ is current, and $R$ is resistance.
3. **Calculate the voltage:**
$$V = (3 + j2)(4 - j3)$$
4. **Multiply the complex numbers:**
$$V = 3 \times 4 + 3 \times (-j3) + j2 \times 4 + j2 \times (-j3)$$
$$V = 12 - j9 + j8 - j^2 6$$
5. **Recall that $j^2 = -1$, so:**
$$V = 12 - j9 + j8 + 6$$
6. **Combine like terms:**
Real part: $12 + 6 = 18$
Imaginary part: $-9j + 8j = -j$
So,
$$V = 18 - j$$
7. **Answer:** The voltage is $18 - j$ volts, which corresponds to option b.)
**Final answer:** $18 - j$ volts.