Question: 14. a) A motor is a combination of resistance and inductive reactance. If a motor has a resistance of 25 Ω and an inductive reactance of 150 Ω, what is the impedance of the motor?
b) If the motor is a 240 V motor, what current does it draw?
1. **State the problem:**
We need to find the impedance $Z$ of a motor with resistance $R = 25$ Ω and inductive reactance $X_L = 150$ Ω, and then find the current drawn by the motor when connected to a voltage $E = 240$ V.
2. **Formula for impedance in series RL circuit:**
$$Z = \sqrt{R^2 + X_L^2}$$
This formula comes from the Pythagorean theorem applied to the resistance and reactance, which are perpendicular components in the impedance triangle.
3. **Calculate impedance:**
$$Z = \sqrt{25^2 + 150^2} = \sqrt{625 + 22500} = \sqrt{23125}$$
4. **Simplify the square root:**
$$Z = 152.07\ \Omega$$
5. **Calculate current drawn using Ohm's law:**
$$I = \frac{E}{Z} = \frac{240}{152.07}$$
6. **Simplify current:**
$$I = 1.58\ \text{A}$$
**Final answers:**
- Impedance $Z = 152.07$ Ω
- Current $I = 1.58$ A
These calculations show how resistance and inductive reactance combine to affect the total impedance and current in an AC motor circuit.