Ohm s Law. Ohmic relationship V=IR. Electric Power. Non Ohmic devises. Schematic representation. Electric Power

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1 Ohm Law Ohmic relationhip V=IR Ohm law tate that current through the conductor i directly proportional to the voltage acro it if temperature and other phyical condition do not change. In many material, the voltage and reitance are connected by Ohm' Law: Ohm' Law : V = IR Conductor which obey Ohm law are made up of metal, carbon and ome alloy. hey are called ohmic conductor. V/volt I/ampere R/ohm V(v) V = IR Slope = V/I = R I(A) Non Ohmic devie Electric Power he connection between voltage and reitance can be more complicated in ome material. hee material are called non-ohmic (e.g. emiconductor device uch a tranitor). We'll focu mainly on ohmic material for now, thoe obeying Ohm' Law. Semiconductor will be covered later on. Worked Example:what i the voltage acro a reitor of K5 when a current of ma flow? V = IR = 500*0.00 =0.V = 00mV Self Aement Quetion: A copper wire ha a length of 60m and a diameter of mm. If the wire i connected to a.5v battery, how much current flow through the wire? Power i the rate at which work i done. It ha unit of Watt. W = J/ Electric power i given by the equation: P =VI. Batterie and power upplie upply power to a circuit, and thi power i ued up by anything that ha reitance. he power diipated in a reitor goe into heating the reitor. In many cae, thi i wated energy. In ome cae, however, the heating i exploited a a ource of heat, uch a in a toater or an electric heater. P = I R ( ince V =IR) Electric Power Schematic repreentation Worked Example: A current of 0mA flow through a reitor when the potential difference acro it i.5v. How much power i diipated in the reitor. P = VI = 0e-*.5 =5mw. Self-aement Quetion: If a light bulb operating at full power of 00W ha a potential difference of 5V acro it. What i the reitance of the bulb. An. R Reitor Battery Reitive circuit Prepared by Dr Yona M Gebremichael, 005

2 Reitor in a circuit Serie configuration Serie connection of reitor Equivalent reitance R Serie connection of reitor he arrow in the above circuit how direction of current flow, by convention the arrow end i at the poitive end. hu the potential at the left end of each reitor i more poitive than at the right, becaue the current i flowing from left to right. In a erie configuration, the ame current flow through each component in the circuit. Reitor in erie Reitor in erie hu we can calculate the voltage drop (potential difference) cro each reitor uing ohm relationhip. V =IR, V =IR, V =IR he total voltage drop acro all the reitor i V +V +V and thi mut be equal to the applied e.m.f auming ideal ource. Hence V V V V V IR IR IR V I ( R ) If V IR IR I ( R ) R i the combinedreitan ce Worked Example: What are the voltage acro R and R? R = R+R = 5k I = V/R = 0/5k = ma hu V = R*I =0k*mA =0v. And V = R*I = 5k*mA =0v. Note that V + V = 0v+0v=0V. Reitor in erie Summary of reitor in erie Self-aement quetion: hree reitor R, R & R of reitance value 00Ω, 00Ω, and 500Ωrepectively are connected in erie acro a 0V e.m.f. ource of negligible internal reitance. By firt drawing a chematic diagram of the circuit, calculate (a) the equivalent reitance, (b)the current flowing in the circuit, (c) the potential difference acro each reitor (d) the power diipated in each reitor and (e) the power taken from the e.m.f. ource. An. a) 800Ω, b).5ma c).5v,.5v, 6.5V d)5.6mw,.mw, 78.mw e)5mw. he reitance equivalent to n number of reitor connected in erie i the um of the individual reitance. Alway check the equivalent reitance i larger than every individual reitor value. Same current flow through each reitor in erie. he voltage drop acro each erie reitor i proportional to it reitance. he um of all the voltage drop acro all the erie reitor i equal to the ource voltage. Prepared by Dr Yona M Gebremichael, 005

3 Reitor in parallel Reitor in parallel Note that the combined reitance i le that either reitance Putting reitor in parallel provide alternative path for the current and lower the effective reitance. Reitor R and R are in parallel he ame voltage act acro each reitor he total current I from the upply equal the um of the eparate current I and I through each reitor. Worked Example: wo reitor of value 0K and 0K are connected in parallel acro a voltage of 5V. What i the value of the current flowing through each reitor. Draw a fully labelled chematic of the circuit. Parallel network Summary of reitor in parallel Self-aement quetion. In the circuit hown below, find the voltage drop acro each reitor. What ingle reitor would replace the network. An. V =.88, V = 0.V, V = V, 840K he reitance equivalent to n number of reitor connected in parallel i the invere of the um of the reciprocal of the individual reitance. Alway check the equivalent reitance i maller than the mallet reitance value in the network. he voltage acro each reitor i the ame for all the reitor in the parallel network. he current through each reitor in parallel i inverely proportional to it reitance. he um of all the current through each reitor i equal to the total current drawn from the ource. he Voltage divider he current divider he potential divider arrangement provide convenient way of getting a variable voltage from a fixed voltage upply. Conider two reitor R and R connected acro emf V. he voltage divider rule tate that the voltage V divide between R and R in the ration of their reitance. he current divider arrangement divide the current between the reitor branche in proportion to their conductance. In the circuit hown I and I are divided in proportion to the conductance of R and R. Prepared by Dr Yona M Gebremichael, 005

4 Variable Reitor Voltage and Current divider Worked Example: Variable reitor alo called pot (hort for potential divider). Unlike the uual reitor (two terminal), thee device have three terminal. wo end terminal are connected and the centre connection, alo called wiper, move the output voltage of the pot from zero to the value of the voltage upplied acro the end of the whole reitive track. A 0k linear pot i ued a a potential divider for a 9V upply. If the wiper i et halfway round the track, what i the voltage when the load reitance i: A. very large B 00K C. 0K Voltage and current divider Meaurement of R,I,V Self-aement quetion: A.5k linear pot i ued a a potential divider for a 9V upply a hown in the figure below. he wiper i et at B 4/5 of the way round from end C of the track. what i the reitance of the length BC of the track? What i the voltage acro BC. If a reitor i connected a a load to X and Y, what doe the voltage become acro BC when the load reitance i (i) 0k (ii) 0k. Comment on the reult. An. k, 0.5k, 7.V, (I) 7V (II) 6V Voltmeter: to meaure the voltage acro a circuit component, the voltmeter i connected acro the component. Voltmeter i connected in parallel. Connecting the voltmeter acro R hould not affect the the quantity under meaurement. In thi cae the voltage drop acro R will not change by connecting the Voltmeter o long a the voltmeter doe not draw any current. hu an ideal voltmeter will have an infinite reitance! Meaurement of V, I & R Which meaurement, V or I? Meauring Current o meaure current, the circuit ha to be broken and an ammeter inerted in the path of the current to be meaured. Ammeter i connected in erie. Addition of the ammeter to the circuit hould not change the quantity to be meaured, in thi cae current. herefore an ideal ammeter mut have zero reitance o it doe not drop and voltage acro it. Which meaurement technique do you think will be the more ueful? Voltage meaurement are ued much more often than current meaurement. he proceing of electronic ignal i uually thought of in voltage term. It i an added advantage that a voltage meaurement i eaier to make. he original circuit doe not need to be changed. Often, the meter probe are connected imply by touching them to the point of interet. 4 Prepared by Dr Yona M Gebremichael, 005

5 Meauring V, I & R Ohm meter: meaure reitance. Ohmmeter work by paing a mall current through the component and meauring the voltage produced. An ohmmeter doe not function with a circuit connected to a power upply. If you want to meaure the reitance of a particular component, you mut take it out of the circuit altogether and tet it eparately. If you try thi with the component connected into a circuit with a power upply, the mot likely reult i that the meter will be damaged. Mot multimeter have a fue to help protect againt miue. he reading will not be accurate. Multimeter Meauring V, I & R A multimeter i a general purpoe electrical meauring intrument which i capable of meauring current and voltage (a.c. and d.c.) and reitance. It ha everal range for each of thee quantitie. Each range ha a different full cale value which can be et by witche. Modern multimeter have auto ranging capability. Moving coil multimeter: diplay the quantity a a mechanical deflection of the pointer acro a graduated cale. Digital multimeter diplay the meaured value a a decimal digit. 5 Prepared by Dr Yona M Gebremichael, 005