In this experiment, you are given three identical 30 Ω resistors. You connects them in four different arrangements and measures the total resistance of each...

(a) The measured resistance for each arrangement is calculated using \( R = \frac{V}{I} \): [2]

Working example: 3 in series: \( R = \frac{2.88}{0.032} = 90 \; \Omega \).

(b) The calculated (theoretical) resistance for each arrangement: [4]

3 in series:

\[ R = 30 + 30 + 30 = 90 \; \Omega \]

3 in parallel:

\[ \frac{1}{R} = \frac{1}{30} + \frac{1}{30} + \frac{1}{30} = \frac{3}{30}, \quad R = 10 \; \Omega \]

1 in series + 2 in parallel: the two parallel resistors give \( R_{\text{pair}} = \frac{30}{2} = 15 \; \Omega \), then in series with the third:

\[ R = 30 + 15 = 45 \; \Omega \]

2 in parallel + 1 in series: electrically identical to the previous arrangement:

\[ R = 15 + 30 = 45 \; \Omega \]

(c) The measured resistance values are equal to (or very close to) the calculated values for all four arrangements. [1] This confirms that the rules for combining resistors in series (\( R_{\text{total}} = R_1 + R_2 + R_3 \)) and in parallel (\( \frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} \)) are correct. [1]

(d) The measured values might differ slightly from the calculated values because of the tolerance (manufacturing variation) in resistor values, contact resistance at the connections, or systematic errors in the ammeter and voltmeter readings. [1]

(e) Switch off the circuit between measurements to prevent the resistors from heating up, which would change their resistance values. Also ensure all connections are secure and use the same battery for all measurements to keep conditions consistent. [1]