A-level Physics (Advancing Physics)/Resistance and Conductance/Worked Solutions

'''1. The potential difference across a resistor is 4V, and the current is 10A. What is the resistance of the resistor?'''

$$R = \frac{V}{I} = \frac{4}{10} = 0.4\mbox{ }\Omega$$

2. What is the conductance of this resistor?

$$G = \frac{1}{R} = \frac{1}{0.4} = 2.5\mbox{ S}$$

'''3. A conductor has a conductance of 2S, and the potential difference across it is 0.5V. How much current is flowing through it?'''

$$ I=GV=2*0.5=1A$$

I = 1A

'''4. A graph is drawn of potential difference across an Ohmic conductor, and current. For every 3 cm across, the graph rises by 2 cm. What is the conductance of the conductor?'''

$$\mbox{Gradient } = \frac{2}{3} = \mbox{ Resistance}$$

$$G = \frac{1}{\frac{2}{3}} = \frac{3}{2} = 1.5\mbox{ S}$$

'''5. On another graph of potential difference and current, the graph curves so that the gradient increases as current increases. What can you say about the resistor?'''

The resistor is not an Ohmic conductor.

'''6. 3 resistors, wired in series, have resistances of 1kΩ, 5kΩ and 500Ω each. What is the total resistance across all three resistors?'''

ΣR = (1 x 103) + (5 x 103) + 500 = 6500Ω = 6.5kΩ

'''7. 2 conductors, wired in parallel, have conductances of 10S and 5S. What is the total resistance of both branches of the parallel circuit?'''

$$G = 10 + 5 = 15\mbox{ S} = \frac{1}{R}$$

$$R = \frac{1}{15} \approx 0.0667\mbox{ }\Omega$$

'''8. The circuit above is attached in series to 1 10Ω resistor. What is the total conductance of the circuit now?'''

$$\Sigma R = 10 + \frac{1}{15} = \frac{151}{15} \mbox{ }\Omega$$

$$G = \frac{15}{151} \approx 0.0993\mbox{ S}$$