Demonstration of Ohm s Law Electromotive force (EMF), internal resistance and potential difference Power and Energy Applications of Ohm s Law

Transcription

1 Lesson 4 Demonstration of Ohm s Law Eectromotive force (EMF), interna resistance and potentia difference Power and Energy Appications of Ohm s Law esistors in Series and Parae Ces in series and Parae Kirchhoff s ues Votage Divider Circuit Measuring Instruments C Circuits Eectroysis Potentiometer ayeigh Potentiometer Wheatstone Bridge Side-Wire (Metre) Bridge

2 EMF, Interna esistance and Potentia Difference The emf of a battery is the maximum possibe votage that the battery can provide between its terminas The e.m.f of this battery is given as I( r) Ir I Ir V ab V ab V dc V ab = V b V a = termina votage (potentia difference across the battery terminas) = externa resistance r = interna resistance

3 Power and Energy The eectrica (potentia) energy, W is the energy gained by the charge Q from a votage source (battery) having a termina votage V. W= QV (the work done by the source on the charge) But Q=It, then W= Vit Unit : Joue (J) The rate of energy deivered to the externa circuit by the battery is caed the eectric power given by, Unit : watt ( 1 W = 1J/s) P VI but V I 2 P I or P 2 V

4 EMF, Power and Energy Exampe: Termina Votage of a Battery (i) (ii) Find the current in the circuit and the termina votage of the battery. Cacuate the power deivered to the oad resistor, the power deivered to the interna resistance of the battery, and the power deivered by the battery. Soution (i) (ii)

5 Ces in series and Parae 1. Current drawn from the ce: = ce emf tota circuit resistance 2. PD across resistors in SEIES with the ce: = ce current x resistance of each resistor 3. Current through parae resistors: = pd across the parae resistors resistance of each resistor

6 Ces in series and Parae TOTAL EMF Case a - Ces connected in the same direction Add emfs together In case a tota emf = 3.5V Case b - Ces connected in different directions Tota emf equas sum of emfs in one direction minus the sum of the emfs in the other direction In case b tota emf = 0.5V in the direction of the 2V ce TOTAL INTENAL ESISTANCE In both cases this equas the sum of the interna resistances

7 Ces in series and Parae In the circuit shown beow cacuate the current fowing and the pd across the 8 ohm resistor 1.5 V 6.0 V 4.0 Ω 8.0 Ω 3.0 Ω Both ces are connected in the same direction. Therefore tota emf = = 7.5V A three resistors are in series. Therefore tota resistance = = 15 Ω Current = I = ε T / T = 7.5 / 15 current = 0.5 A PD across the 8 ohm resistor = V 8 = I x 8 = 0.5 x 8 pd = 4 V

8 Ces in series and Parae For N identica ces each of emf ε and interna resistance, r Tota emf = ε Tota interna resistance = r / N The ost vots = I r / N and so ces paced in parae can deiver more current for the same ost vots due to the reduction in interna resistance.

9 esistors in Series and Parae

10 esistors in Series and Parae The inverse of the equivaent resistance of two or more resistors connected in parae is equa to the sum of the inverses of the individua resistances. Furthermore, the equivaent resistance is aways ess than the smaest resistance in the group.

11 esistors in Series and Parae Cacuate the potentia difference across and the current through the 6 ohm resistor in the circuit beow. Tota resistance of the circuit = 8 Ω in series with 12 Ω in parae with 6 Ω = = Ω 8 Ω 9 V 12 Ω Tota current drawn from the battery = V / T = 9V / Ω = A pd across 8 Ω resistor = V 8 = I 8 = A x 8 Ω = 5.40 V therefore pd across 6 Ω (and 12 Ω) resistor, V 6 = pd across 6 Ω resistor = 3.6 V Current through 6 Ω resistor = I 6 = V 6 / 6 = 3.6 V / 6 Ω current through 6 Ω resistor = A

12 Kirchhoff s ues There are ways in which resistors can be connected so that the circuits formed cannot be reduced to a singe equivaent resistor Two rues, caed Kirchhoff s ues can be used instead (i) Junction ue The sum of the currents entering any junction must equa the sum of the currents eaving that junction A statement of Conservation of Charge (ii) Loop ue The sum of the potentia differences across a the eements around any cosed circuit oop must be zero A statement of Conservation of Energy

13 Kirchhoff s ues I 1 = I 2 + I 3 From Conservation of Charge Diagram b shows a mechanica anaog

14 Kirchhoff s ues Assign symbos and directions to the currents in a branches of the circuit If a direction is chosen incorrecty, the resuting answer wi be negative, but the magnitude wi be correct When appying the oop rue, choose a direction for transversing the oop ecord votage drops and rises as they occur

15 Traveing around the oop from a to b In a, the resistor is transversed in the direction of the current, the potentia across the resistor is I In b, the resistor is transversed in the direction opposite of the current, the potentia across the resistor is +I Kirchhoff s ues

16 In c, the source of emf is transversed in the direction of the emf (from to +), the change in the eectric potentia is +ε In d, the source of emf is transversed in the direction opposite of the emf (from + to -), the change in the eectric potentia is -ε Kirchhoff s ues

17 Kirchhoff s ues Use the junction rue as often as needed, so ong as, each time you write an equation, you incude in it a current that has not been used in a previous junction rue equation In genera, the number of times the junction rue can be used is one fewer than the number of junction points in the circuit

18 Kirchhoff s ues The oop rue can be used as often as needed so ong as a new circuit eement (resistor or battery) or a new current appears in each new equation You need as many independent equations as you have unknowns

19 Votage Divider Circuit v i i i( ) Identify the current and Appy KVL S v O v eq O 1 2 eq 1 eq 2 L L v S L v S i v S v1 i1 vs v2 i2 vs 1 2 v L O, 2 1 2

20 Potentiometer A potentiometer is mainy used to measure potentia difference. It consists of a uniform wire. Basicay a potentiometer circuit consists of a uniform wire AB of ength 100.0cm, connected in series to a driver ce with emf V of negigibe interna resistance. Potentiometer can be used to : i) Measure an unknown e.m.f. of a ce. ii) Compare the e.m.f.s of two ces. iii) Measure the interna resistance of a ce.

21 V Potentiometer (Driver ce -accumuator) I I A + - V x (Unknown Votage) G C I Jockey I B The potentiometer is baanced when the jockey (siding contact) is at such a position on wire AB that there is no current through the gavanometer. Thus Gavanometer reading = 0 When the potentiometer in baanced, the unknown votage (potentia difference being measured) is equa to the votage across AC. V AC AC AB V V AB AC AB AB V x V AC

22 Potentiometer V When the potentiometer is baanced, I G = 0 I A 2 1 I ε 1 ε 2 C J (1) S (2) D G I I B Baance ength, AC = 1 for ε 1 and AD = 2 for ε V AC AB AD AB AB 1 V V 1 Hence 1 AB 2 AB AB 2 V V

23 ayeigh Potentiometer

24 ayeigh Potentiometer

25 Wheatstone Bridge It is used to measure the unknown resistance of the resistor. Figure beow shows the Wheatstone bridge circuit consists of a ce of e.m.f. (accumuator), a gavanometer, known resistances ( 1, 2 and 3 ) and unknown resistance x. The Wheatstone bridge is said to be baanced when no current fows through the gavanometer this can be achieved by adjusting 3. Hence I I 11 I23 12 I2X Potentia at C = Potentia at D X 2 1 3

26 Wheatstone Bridge Aternative Wheatstone Bridge proof

27 Side-Wire (Metre) Bridge

28 Charging a Capacitor C Circuits

29 Charging a Capacitor C Circuits

30 C Circuits Charging a Capacitor Pots of capacitor charge and circuit current versus time are shown in the Figure Note that the charge is zero at t = 0 and approaches the maximum vaue Cε as t The current has its maximum vaue I 0 = ε/ at t = 0 and decays exponentiay to zero as t. The quantity C, which appears in the exponents is caed the time constant τ of the circuit. It represents the time interva during which the current decreases to 1/e of its initia vaue; that is, in a time interva

31 C Circuits Discharging a Capacitor

32 C Circuits Exampe: Charging a Capacitor in an C Circuit An uncharged capacitor and a resistor are connected in series to a battery,. If ε= 12.0 V, C = 5.00 μf, and = 8.00 x 10 5 Ω, find the time constant of the circuit, the maximum charge on the capacitor, the maximum current in the circuit, and the charge and current as functions of time.

33 C Circuits Consider a capacitor of capacitance C that is being discharged through a resistor of resistance, as shown in the Figure beow (i) After how many time constants is the charge on the capacitor onefourth its initia vaue? (ii) The energy stored in the capacitor decreases with time as the capacitor discharges. After how many time constants is this stored energy onefourth its initia vaue? Soution (i) (ii)

34 Eectroysis The chemica Effect of Current Eectroysis is the breakdown of a substance by eectricity Eectroyte - a moten or aqueous soution through which an eectrica current can fow. Eectroytes contain positive and negative ions. During eectroysis, positive and negative eectrodes are put into the eectroyte. The positive eectrode is caed the anode. The negative eectrode is caed the cathode. The negative ions (caed anions) are attracted to the anode. At the anode, the negative ions ose eectrons to become atoms/moecues. The positive ions (caed cations) are attracted to the cathode. At the cathode, the positive ions gain eectrons to become atoms/moecues

35 Eectroysis

36 Eectroysis