P.1 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources Car dashboard Resistance of ammeters Resistance of voltmeters Check-point 9 Internal resistance of power sources Check-point Resistance of ammeters, voltmeters and power sources

P.2 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources Car dashboard Some cars have special ammeters and voltmeters on their dashboard. What do ammeter and voltmeter measure? Current and voltage of the car battery.

P.3 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources 1 Resistance of ammeters Using an ammeter to measure current Expt 2f In earlier units, we have assumed batteries, ammeters and voltmeters are all ideal. In reality, they do have resistance. Let us investigate the effect of their internal resistance in practice.

P.4 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources Experiment 2f Using an ammeter to measure current 2.7 Expt 2f - Using an ammeter to measure current 1.Connect the circuit. 2.Record the reading of ammeter I ’. 3.Calculate the theoretical value of the current I and compare it with the experiment value I ’. Video

P.5 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources 1 Resistance of ammeters A practical ammeter has an internal resistance instead of 0. When connected in series, equivalent resistance  R eq = R + R A  measured current I ’ < theoretical value I

P.6 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources 1 Resistance of ammeters If the ammeter has very low resistance, no significant reduction in measurement A good ammeter has a very low resistance.

P.7 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources 1 Resistance of ammeters Typical values of internal resistance of ammeters: Range of ammeter Typical internal resistance (may vary by a factor of 10) 0–1 A 0.1  0–1 mA 100  0–100 µA 1 k  Internal resistance of ammeter << resistance in circuit  Measured current  theoretical current Connecting an ammeter directly to a battery Example 12

P.8 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources Example 12 Connecting an ammeter directly to a battery Why should we not connect an ammeter with range 0–1 A directly across the terminals of a battery?  Ammeter has an extremely small resistance  large current will draw from the battery  could damage the ammeter

P.9 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources 1 Resistance of ammeters Compare the accuracy of two ammeters Example 13

P.10 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources Example 13 Compare the accuracy of two ammeters To compare current measured by A and B, a resistor of 21  is connected to a 3-V battery and the ammeters are connected to circuit in series in turn. Ammeter AAmmeter B Range0–1 A0–200 mA Internal resistance 0.1  2 

P.11 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources Example 13 Compare the accuracy of two ammeters I = VRVR 3 21 = = A (a) Theoretical value I through the resistor = ? (b) (i)Find the value of the measured current if the ammeter used is A. Let internal resistance of A be R A and current measured by A be I ’. VR + RAVR + RA I ’ = = = A

P.12 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources Example 13 Compare the accuracy of two ammeters (b) (ii)Find the value of the measured current if the ammeter used is B. Let internal resistance of B be R B and current measured by B be I ’’. VR + RBVR + RB I ’’ = = = A (c) Which ammeter is more accurate? Ammeter A ( ∵ smaller internal resistance)

P.13 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources 2 Resistance of voltmeters Using a voltmeter to measure voltage across resistors Expt 2g

P.14 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources Experiment 2g Using a voltmeter to measure voltage across resistors 2.8 Expt 2g - Using a voltmeter to measure voltage across resistors 1.Connect the circuit. 2.Record the voltmeter reading V ’. 3.Calculate theoretical value of voltage V and compare it with the experiment value V ’. Video

P.15 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources 2 Resistance of voltmeters Practical voltmeter has a large internal resistance but not infinite. When connected in parallel,  equivalent resistance across R 1.  measured voltage V ’ < theoretical value V 1 R eq 1R11R1 1RV1RV = +

P.16 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources 2 Resistance of voltmeters A good voltmeter has a very high resistance. Very high resistance of voltmeter  No significant reduction in measurement

P.17 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources 2 Resistance of voltmeters Some typical values of the internal resistance of voltmeters: Range of voltmeterTypical internal resistance 0–0.1 V 1 k  0–1 V 10 k  0–10 V 100 k  How voltmeters affect the reading of voltage Example 14

P.18 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources Example 14 How voltmeters affect the reading of voltage Voltmeter AVoltmeter B Range0–0.1 V0–1 V Internal resistance 1 k  10 k  To compare the voltage measured by voltmeters A and B, resistors R X (240  ) and R Y (360  ) are connected to a dynamo of 200 mV.

P.19 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources Example 14 How voltmeters affect the reading of voltage (a) Theoretical value of voltage V X across R X = ? VRX + RYVRX + RY I = = = 3.33  10 –4 A V X = IR X = 3.33  10 –4  240 = 80 mV

P.20 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources Example 14 How voltmeters affect the reading of voltage V R eq ’ + R Y I’ = = = 3.61  10 –4 A = I’ R eq ’ = 3.61  10 –4  194 = 70.1 mV = 194  Measured voltage (b)(i) If A is used, measured voltage across X = ? Equivalent resistance of R X and R A = R eq ’ Current through A = I ’ = + –1 1RX1RX 1RA1RA R eq ’ = + –1

P.21 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources Example 14 How voltmeters affect the reading of voltage V R eq ’’ + R Y I’’ = = = 3.37  10 –4 A = 234  (b)(ii) If B is used, measured voltage Y = ? Equivalent resistance of R X and R B = R eq ’’ Current through B = I’’ = I’’ R eq ’’ = 3.37  10 –4  234 = 78.8 mV Measured voltage 1RX1RX 1RB1RB R eq ’’ = + – = + –1

P.22 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources Example 14 How voltmeters affect the reading of voltage (c) Which voltmeter gives a more accurate result? Voltmeter B ( ∵ higher internal resistance) Theoretical value80 mV Measured by A70.1 mV Measured by B78.8 mV

P.23 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources Check-point 9 – Q1 In the circuit, ammeters and resistors of different resistance are used. Which combination gives the most unreliable current reading? RARRAR A1  5  B0.1  5  C1  100 

P.24 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources Check-point 9 – Q2 In the circuit, voltmeters and resistors of different resistance are used. Which combination gives the most unreliable voltage reading? RVRRVR A1 k  5 k  B1 k  50  C100 k  5 k 

P.25 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources Check-point 9 – Q3 Two ammeters (with R = 6  and 6 M  ) are used to measure the current through the bulb.

P.26 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources Check-point 9 – Q3 (a) Complete the table. ideal R = 6  R = 6 M  Ammeter readings Voltmeter readings 1 A 0.6 A 1.50  A 6 V 3.6 V 9.00  V (b) Good ammeters have ______ resistance. low

P.27 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources Check-point 9 – Q4 Two voltmeters (with R = 6  and 6 M  ) are used to measure the voltage across the bulb.

P.28 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources Check-point 9 – Q4 (a) Complete the table. ideal R = 6  R = 6 M  Ammeter readings Voltmeter readings 1 A 1.5 A1.00 A 6 V 4.5 V 6.00 V (b) Good voltmeters have ______ resistance. high

P.29 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources 3 Internal resistance of power sources E.m.f. of a power supply Expt 2h

P.30 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources Experiment 2h E.m.f. of a power supply 2.9 Expt 2h - E.m.f. of a power supply 1.Connect a circuit. Record the reading of voltmeter. 2.Connect a ‘12 V, 24 W’ lamp across the power supply and record the reading of voltmeter. 3.Find the drop in voltage and estimate internal resistance of power supply. Video

P.31 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources 3 Internal resistance of power sources The voltage across the power supply drops when the lamp is connected. All power supplies (e.g. batteries and low voltage power packs) have internal resistance. ( ∵ internal resistance of power supply)

P.32 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources 3 Internal resistance of power sources The voltmeter reads 12 V when it is connected directly across a 12-V power supply. After a lamp is connected, reading  slightly New reading  terminal voltage

P.33 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources  potential drop across internal resistance of power supply  Internal resistance shares voltage of 3.5 V  The lamp has a terminal voltage of 8.5 V 3 Internal resistance of power sources Terminal voltage (V ) across the power supply < e.m.f Internal resistance of a battery Video

P.34 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources 3 Internal resistance of power sources I : current through the circuit r : internal resistance of the power source Resistance of a dry cell: typically ~ 0.5  Resistance of a 0–12 V power pack: ~ 2–3  E.m.f. of a power source terminal voltage across the power source voltage across its internal resistance = + e.m.f. = V + Ir

P.35 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources Check-point 10 – Q1 Consider the resistance of battery: (a) How would it affect the circuit if batteries with resistance 6  and 6 M  were used? ideal R = 6  R = 6 M  Ammeter readings Voltmeter readings 1 A 0.6 A 1.50  A 6 V 3.6 V 9.00  V (b) A good battery should have a ______ resistance. low

P.36 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources 3 Internal resistance of power sources Measuring small resistance Example 15

P.37 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources Example 15 Measuring small resistance Joe uses voltmeter-ammeter method to verify the resistance of a 10-  light bulb. Internal resistance: ammeter = 2  voltmeter = 1 k  power supply = 2  (a)He first sets up a circuit as shown.

P.38 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources Example 15 Measuring small resistance (a) (i) Measured current I 1 = ? 1 R eq ’ 1 R A + R 1RV1RV = = +  R eq ’ = 11.9  V R eq ’ + r I 1 = = = A Let the equivalent resistance of light bulb, ammeter and voltmeter be R eq ’.

P.39 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources Example 15 Measuring small resistance (a) (ii) Measured voltage V 1 = ? V 1 = e.m.f. – I 1 r = 2 – (0.144)(2) = 1.71 V (iii) Measured resistance of bulb  R 1 = ? R 1 = V1I1V1I1 = 11.9  =

P.40 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources Example 15 Measuring small resistance (i) Measured current I 2 = ? = + 1 R eq ’’ 1R1R 1RV1RV = +  R eq ’’ = 9.90  V R A + R eq ’’ + r I 2 = = = A (b) The circuit is rearranged: Let the equivalent resistance of light bulb and voltmeter be R eq ’’.

P.41 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources Example 15 Measuring small resistance (b) (ii) Measured voltage V 2 = ? V 2 = e.m.f. – I 2 (r + R A ) = 2 – (0.144)(2 + 2) = 1.42 V (iii) Measured resistance of bulb R 2 = ? R 2 = V2I2V2I2 = 9.86  =

P.42 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources Example 15 Measuring small resistance (c) Why are the measured resistance and its true value different  in both cases? Case 1: Voltmeter measures the total voltage across light bulb & ammeter. (Correct I, incorrect V  incorrect R ) Case 2: Ammeter measures the total current through light bulb & voltmeter. (Incorrect I, correct V  incorrect R )

P.43 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources Example 15 Measuring small resistance (d) Which setting is better? Why? Case 2 is better. In case 1, resistances of light bulb and ammeter are comparable.  Voltages across them are also comparable. ∴ Voltmeter reading has a large error. In case 2, resistance of voltmeter >> that of light bulb.  Current through voltmeter is very small. ∴ Ammeter reading has a small error.

P.44 Book 4 Section 2.5 Resistance of ammeters, voltmeters and power sources The End