State one S.I. base quantity other than length, mass, and time.
The figure below shows two resistors, PPP and QQQ, connected in series.
The resistors are wires made of the same material of resistivity ρ\rhoρ. Both wires have the same length LLL. Wire PPP has a diameter ddd and wire QQQ has a diameter 2d2d2d.
Show that the total resistance RRR of the series combination is given by the equation:
R=5ρLπd2 R = \frac{5\rho L}{\pi d^2} R=πd25ρLA student uses this equation to determine RRR. The table below shows the data recorded by the student in her lab book:
| Quantity | Value |
|---|---|
| ρ\rhoρ | 1.2×10−6 Ω m1.2 \times 10^{-6}\ \Omega\text{ m}1.2×10−6 Ω m |
| LLL | 60.0±0.5 cm60.0 \pm 0.5\text{ cm}60.0±0.5 cm |
| ddd | 0.400±0.005 mm0.400 \pm 0.005\text{ mm}0.400±0.005 mm |
Name the likely instruments used by the student to measure LLL and ddd.
Use the data in the table to determine RRR and its absolute uncertainty. Write your answer to the correct number of significant figures.
The instrument used to measure the diameter ddd has a systematic zero error such that the measured value of ddd is smaller than the actual value. Discuss how the actual value of RRR compares with the value calculated in part 2.
