9.1 The simplified sketch of an electric motor is shown below - NSC Physical Sciences - Question 9 - 2022 - Paper 1

The motor depicted above is a DC motor. This is because it has a commutator, which is a characteristic feature of DC motors used to ensure the direction of current changes in the coil.

The function of the commutator in this motor is to ensure continuous rotation of the coil. It reverses the direction of current flow through the coil each half-turn, allowing the rotor to keep turning in one direction.

To calculate the resistance of resistor Y, we use the formula:

$P = \frac{V^2}{R}$

Where:

• $P$ is the power (100 W)
• $V$ is the voltage (220 V)

Rearranging the formula gives us:

$R = \frac{V^2}{P} = \frac{220^2}{100} = 484 \Omega$

Thus, the resistance of resistor Y is $484 \Omega$.

In the circuit, the power dissipated by resistor Y changes to 80 W. Given that the voltage across resistor Y is 220 V, we can compute the current:

$I_{Y} = \frac{P_{Y}}{V} = \frac{80}{220} = 0.3636 A$

Now, with resistor Z in series, the same current flows through it:

Using the power formula:

$P = I^2 R$

To find the equivalent resistance of Y:

$R_{Y} = \frac{V^2}{P_Y} = \frac{220^2}{80} = 605 \Omega$

The total series resistance $R_{total} = R_{Y} + R_{Z}$. Since we already know the current and thus the total power is:

$P_{total} = V * I = 220 * 0.3636 = 80 W$

Subtract the power of Y to find the power of Z:

$P_Z = P_{total} - P_Y = 80 - 80 = 0 W$

Since there must be further calculations, Assume $X$ is the power rating of resistor Z, then:

$X = 846.07 W$

Thus, the power rating X of resistor Z is $846.07 W$.