Graphical uncertainties exercise

 

Worksheet on Capacitors

Capacitors

 

1 A capacitor has a charge of 20 μC (microcoulomb) when a p.d. of 200 V is applied to it. Calculate the capacitance of the capacitor. 1x10^-7F

What is the charge on the capacitor if a battery of 40 V is connected?

          4 x10^-6C
2 Define capacitance, microfarad. Calculate the p.d. across a 2 μF capacitor if it has a charge of 80 μC. 40V Calculate the new p.d. if the capacitor is then connected to an uncharged capacitor of 4 μF. 13.3V What is the charge on each capacitor in this case? 2.7 x10^-5 C, 5.3 x10^-5 C

3 Calculate the combined capacitance of (i) 2 μF and 3 μF capacitor in series, 1.2 μF (ii) a 4 μF capacitor in series with a parallel arrangement of a 3 μF and 2 μF capacitor. 2.2 μF Prove from first principles the formula 4 for the combined capacitance of two capacitors in series and in parallel.

4 A capacitor of 2 μF is charged by a 100 V battery. Calculate the energy in the capacitor. 1 x10^-2 J If the capacitor is disconnected from the battery and then connected to a 6 μF uncharged capacitor, find the new energy in each capacitor 6.3 x10^-4 J, 1.9 x10^-3 J. Account for the loss in energy which has occurred. Heat lost as current passes through external in circuit, (resistance of wires)

 

Fig 3

5 A capacitor of 4 μF is (i) in parallel, 4.8 x10^-4 C 7.2 x10^-4 C (ii) in series with a 6 μF capacitor, 2.9 x10^-4 C and a battery of 120 V is connected across the arrangement in each case Calculate the charge on each capacitor, and the total energy of the capacitors in both cases. Parallel 72mJ Series 17.2mJ

6 Two capacitors of 25 μF and 100 μF respectively are joined in series with a d.c. supply of 6.0 V. Fig 3 (i) What is the charge on each capacitor and the p.d. across each? 1.2 x 10^-4 C, 4.8V, 1.2V
The supply is now disconnected without affecting the charge on each capacitor. Their two positive plates, and their two negative plates, are then connected together Fig. 3 (ii). Calculate (i) the common p.d. of the capacitors, 1.92 V(ii) the loss in energy of the two capacitors. 1.3 x10^-4 J. How is this loss of energy accounted for?
7 A 100 V supply is connected to a 4 μF capacitor in series with a 2 MΩ (2 million ohms) resistor. Find (i) the current I at the instant of switching on the supply 5 x10^-5A, (ii) the final charge on the capacitor4 x10^-4C, (iii) the time taken to charge the capacitor assuming the mean value of the current during flow of charge is I/2. 16s (I do know of the approximation of 5RC, but you have to use the information in the question)
8 A 25 μF capacitor, previously charged by a p.d. of 10 V, is discharged through a 2 MΩ(2 x 10⁶Ω) resistor. What is: (i) the initial charge on the capacitor 2.5 x10^-4C  (ii) the initial current? 5 x10^-6 A

Uncertainties

 

Uncertainties

Estimate the uncertainty of your protractor.  1⁰ or 0.5⁰

Try and find your pulse. Then count how many beats per minute. Estimate the uncertainty. 1 bpm

How would you quote the following results from a repeated experiment?

2.00cm, 19.8cm, 1.99cm, 2.02cm, 197mm, 2.01cm  2.00+/-0.02cm

The length of a wooden block is found by placing it against a 30cm ruler (calibrated in mm). One end is judged to be nest to 62mm on the scale. The other end is nest to 1.5 cm on the scale. What is the length of the block? What is the uncertainty in the length? 4.7 cm If you take the uncertainty of your measure met to be 0.1cm then your total uncertainty is 0.2cm (1mm either end)

Three sets of students measure the value of g in the laboratory. Group 1 use a pendulum, group 2 use light gates, group 3 use a stopwatch and ruler and calculate the acceleration of a falling ball. Their results are below. All values in ms^-2

Group	1	2	3	4	5	mean g
1	9.79	9.87	9.76	9.79	9.78	9.798
2	9.67	9.66	9.66	9.68	9.67	9.668
3	7.48	8.97	10.32	11.61	10.67	9.81

 

Calculate the mean values. Plot all 3 groups’ results on a scatter graph.

Which is the most accurate?  Group 3 – nearest accepted value

Which is the most precise?          Group 2 – least scatter in results.

Which is the best experimental method? Group 1 good accuracy and precision

Group 3 has good accuracy but high scatter so random error - poor experiment probably due to method.

Group 2 has good precision but poor accuracy, probably due to systematic error – again poor experiment probably due to equipment

Give reasons for your answers.

A ring has an inner radius of , nd an outer radius of

.  

What is the width of the ring? Width = 8.0 -5.0 = 3.0 mm

Calculate the maximum and minimum width.

(8.0 + 0.2) – (5 – 0.2) = 3.4mm   (8.0 -0.2) – (5 + 0.2) = 2.6mm

So range of possible values is 2.6 -3.4 = 0.8mm.

Then state the uncertainty.

So width is  3.0+/- 0.4 mm (i.e. a spread of 8mm around the 3.0)

What is the uncertainty in the size of the hole? Holes don’t exist.

 

A set of students independently measure the period of a pendulum and obtain the following results

What would be quoted as the period and the uncertainty?   1.01+/-0.02s

Prefixes Prep answers

Prefixes worksheet

Mathematical Prefixes

Prefix	Symbol	Name	Multiplier
femto	f	quadrillionth	10-15
pico	p	trillionth	10-12
nano	n	billionth	10-9
micro	µ	millionth	10-6
milli	m	thousandth	10-3
kilo	k	thousand	103
mega	M	million	106
giga	G	billion	109
tera	T	trillion	1012
peta	P	quadrillion	1015

When you are given a variable with a prefix you must convert it into its numerical equivalent in standard form before you use it in an equation. 

Convert the following:

 

1.4 kW = 1.4x10³W                                                                       10 μC = 10x10^-6C

 

24 cm = 24x10^-2m                                                                            340 MW = 3.40x10⁸W

 

46 pF = 46x10^-12F                                                                            0.03 mA = 0.03x10^-3A

 

52 Gbytes = 52x10⁹bytes                                                              43 kΩ =  43x10³Ω

 

0.03 MN =   0.03x10⁶N                                                                  83 Pm = 83x10¹⁵m

 

 

Now convert between different prefixes

 

5.46m to cm =   546cm                                                 65mm to m = 0.065m

 

 

3cm to m = 0.03m                                                           0.98m to mm = 980mm

 

 

34kW to GW =   0.000034GW = 34x10^-6GW        76nN to kN = 76x10^-12kN

Challenge Task

1. What is 5.2 mm³ in m³?

5.2x10-9m³

 

 

2. What is 24cm² in m²?

24x10^-4m²

 

 

3. What is  0.96 x 10⁶ m² in km²?

0.96km²