# Circuits. PHY2054: Chapter 18 1

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1 Circuits PHY2054: Chapter 18 1

2 What You Already Know Microscopic nature of current Drift speed and current Ohm s law Resistivity Calculating resistance from resistivity Power in electric circuits PHY2054: Chapter 18 2

3 Chapter 18: Electric Circuits Work, energy and EMF Single loop circuits Multiloop circuits Ammeters and voltmeters RC circuits and time constant PHY2054: Chapter 18 3

4 Reading Quiz for Chapter 18 When resistors are connected in series (1) the current in each resistor is different (2) the current in each resistor is the same (3) the voltage in each resistor is the same Which of the following is not related to Kirchhoff s Rules? (1) conservation of charge (2) conservation of energy (3) conservation of momentum PHY2054: Chapter 18 4

5 Resistors in series EMF of battery is 12 V, 3 identical resistors. What is the potential difference across each resistor? 12 V 0 V 3 V 4 V Equal resistances, 4V across each one PHY2054: Chapter 18 5

6 Resistors in series All light bulbs are identical in these two circuits. Which circuit has the higher current? circuit A circuit B both the same Which circuit has larger total brightness? circuit A circuit B both the same Current in A is twice that of B Brightness in each bulb in B is ¼ A so total brightness of B is ½ A A B PHY2054: Chapter 18 6

7 Real EMF Sources: Internal Resistance Real batteries have small internal resistance Lowers effective potential delivered to circuit i V 0 = r + R Vb r V a V 0 V = V V = V ir eff b a 0 V 0 = V0 r + R r V eff R C C V0 = 1 + r / R This is the voltage measured across the terminals! PHY2054: Chapter 18 7

8 Internal Resistance Example Loss of voltage is highly dependent on load V 0 = 12V, r = 0.1Ω, R = 100Ω Loss of 0.01V V 0 = 12V, r = 0.1Ω, R = 10Ω Loss of 0.1V V 0 = 12V, r = 0.1Ω, R = 1Ω Loss of 1.1V V 0 = 12V, r = 0.1Ω, R = 0.5Ω Loss of 2.0V V eff V0 = 1 + r / R V eff = 12/1.001 = V V eff = 12/1.01 = 11.9 V V eff = 12/1.1 = 10.9 V V eff = 12/1.2 = 10.0 V PHY2054: Chapter 18 8

9 Heating From Internal Resistance Heating of EMF source: P = i 2 r Heating is extremely dependent on load You can feel battery warm when it is used at high current V ba V 0 = 12V, r = 0.1Ω V0 = 1 + r / R R = 100Ω V ba = 11.99V i = 0.12 A P = W R = 10Ω V ba = 11.9V i = 1.19 A P = 0.14 W R = 1.0Ω V ba = 10.9V i = 10.9 A P = 11.9 W R = 0.5Ω V ba = 10.0V i = 20 A P = 40 W V 0 i = r + R 2 P= i r PHY2054: Chapter 18 9

10 Resistors in Parallel Current splits into several branches. Total current is conserved i = i 1 + i 2 Potential difference is same across each resistor V = V 1 = V 2 V V V = + R R R p = + R R R p 1 2 R p = equivalent resistance V V a d a d I I I I I 1 I 2 R 1 R 2 I R p PHY2054: Chapter 18 10

11 As more resistors R are added in parallel to the circuit, how does total resistance between points P and Q change? (a) increases (b) remains the same (c) decreases Resistors in Parallel If the voltage between P & Q is held constant, and more resistors are added, what happens to the current through each resistor? (a) increases (b) remains the same (c) decreases Overall current increases, but current through each branch is still V/R. PHY2054: Chapter 18 11

12 Devices added in parallel Each device sees full 120 V Each current is i = 120/R i Household Circuits Overload: too many devices can draw more current than house wires can handle. Overheating of wires Fire hazard! Circuit breaker protects against this happening PHY2054: Chapter 18 12

13 Example: Equivalent Resistance What is the net resistance of the circuit connected to the battery? Each resistance has R = 3Ω R 1, R 2 in series R 12 = 6Ω R 3 in parallel with R 12 R 123 = 2Ω R 4 in series with R 123 R 1234 = 5Ω R 5 in parallel with R 1234 R = 1.875Ω R 6 in series with R R = 4.875Ω PHY2054: Chapter 18 13

14 Circuits If the light bulbs are all the same in each of these two circuits, which circuit has the higher current? (a) circuit A B draws twice the (b) circuit B current as A (c) both the same In which case is each light bulb brighter? (a) circuit A (b) circuit B (c) both the same Current through each branch is unchanged (V/R) A B PHY2054: Chapter 18 14

15 Light Bulb Problem Two light bulbs operate at 120 V, one with a power rating of 25W and the other with a power rating of 100W. Which one has the greater resistance? (a) the one with 25 W (b) the one with 100 W (c) both have the same resistance Which carries the greater current? (a) the one with 25 W (b) the one with 100 W (c) both have the same current P = I 2 R = V 2 /R, where V is the same for both. 100W bulb has ¼ the resistance of the 25W bulb and carries 4x the current. PHY2054: Chapter 18 15

16 Dimmer Assume a dimmer consisting of a variable resistor is put in series with a bulb. When you rotate the knob of a light dimmer, what is being changed in the electric circuit? (a) the voltage in the circuit (b) the resistance (c) the current House voltage is always ~120 V. (d) both (a) and (b) Turning the knob increases the circuit (e) both (b) and (c) resistance and thus lowers the current. Note that this is a bad design for a Dimmer. Why? PHY2054: Chapter 18 16

17 Power lines At large distances, the resistance of power lines becomes significant. To transmit maximum power, is it better to transmit high V, low I or high I, low V? (a) high V, low I (b) low V, high I (c) makes no difference Power loss is I 2 R, so want to minimize current. Why do birds sitting on a high-voltage power line survive? They are not touching high and low potential simultaneously to form a circuit that can conduct current PHY2054: Chapter 18 17

18 Resistors Current flows through a light bulb. If a wire is now connected across the bulb as shown, what happens? (a) Bulb remains at same brightness (b) Bulb dims to 1/4 its former brightness (1/2 current) (c) Bulb goes out (d) None of the above The wire shunt has almost no resistance and it is in parallel with a bulb having resistance. Therefore voltage across shunt (and bulb ) is ~ 0. Thus almost all the current follows the zero (or extremely low) resistance path. PHY2054: Chapter 18 18

19 Circuits Two light bulbs A and B are connected in series to a constant voltage source. When a wire is connected across B, what will happen to bulb A? (a) burns more brightly than before (b) burns as brightly as before (c) burns more dimly than before (d) goes out The wire shunt effectively eliminates the second resistance, hence increasing the current in the circuit by 2x. The first bulb burns 4x brighter (I 2 R). PHY2054: Chapter 18 19

20 Circuits Consider the network of resistors shown below. When the switch S is closed, then: What happens to the voltage across R 1, R 2, R 3, R 4? What happens to the current through R 1, R 2, R 3, R 4? What happens to the total power output of the battery? Let R 1 = R 2 = R 3 = R 4 = 90 Ω and V = 45 V. Find the current through each resistor before and after closing the switch. Before I 1 = 45/135 = 1/3 I 2 = 0 I 3 = I 4 = 15/90=1/6 After I 1 = 45/120 = 3/8 I 2 = I 3 = I 4 = 1/8 PHY2054: Chapter 18 20

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