Simple Resistive Circuits - Introduction to Electrical Engineering - Lecture Slides, Slides of Electrical Engineering

Download Simple Resistive Circuits - Introduction to Electrical Engineering - Lecture Slides and more Slides Electrical Engineering in PDF only on Docsity! Circuit Analysis Lecture 03 - Simple Resistive Circuits and Applications Docsity.com Calculating Resistance Area, A l lR A ρ ⋅ = 6 6 1.67 10 2.70 10 cu al cm cm ρ ρ − − = ⋅ Ω ⋅ = ⋅ Ω ⋅ When conductor has uniform cross-section Docsity.com Resistors in Parallel (1/2) I s R1 R2 + V1 - I 1 I 2+ V2 - + Vs - + Vs - I s Req 1 1 1 VI R = 22 2 VI R = By KVL: Vs = V1 = V2 By KCL: Is = I1 + I2 By Ohm’s Law: and Combine: 1 2 1 2 1 2 1 1 s s s eq VV VI V R R R R R   = + = + =    Docsity.com Resistors in Parallel (2/2) 1 2 1 2 eq R RR R R = + 1 2 1 1 1 1 eq nR R R R = + + + 1 2eq nG G G G= + + + For two resistors: For many resistors: In terms of conductance: Docsity.com Voltage Divider Circuit Vs R1 R2 + V1 - + V2 - M easure V2 I ( )1 2sV I R R= + 1 2 sVI R R = + 2 2 2 2 1 2 1 2 s s V RV I R R V R R R R = ⋅ = = + + Docsity.com Current Divider Circuit I s G1 G2 + vo - i1 i2 1 2 1 2 1 2 s o Ii iv G G G G = = = + 2 2 2 1 2 1 2 1 1 1s s G Ri I I G G R R = = + + 2 1 2 1 2 1 2 1 2 1 2 1 1 1s s R R R Ri I I R R R RR R = = ++ If there are only two paths: In general: 1 2 n n s n Gi I G G G = + + + Docsity.com D’Arsonval Meter Movement • Permanent Magnet Frame • Torque on rotor proportional to coil current • Restraint spring opposes electric torque • Angular deflection of indicator proportional to rotor coil current S N Docsity.com D’Arsonval Voltmeter • Small voltage rating on movement (~50 mV) • Small current rating on movement (~1 mA) • Must use voltage dropping resistor, Rv Rv + Vd'A - + VRv -+ Vx - Id'A Docsity.com D’Arsonval Ammeter • Small voltage rating on movement (~50 mV) • Small current rating on movement (~1 mA) • Must use current bypass conductor, Ga Ga + Vd'A - IGa Id'AIx Docsity.com Example: 1 Amp F.S. Ammeter Note: d’Arsonval movement has conductance of 0.02 S Scale chosen for 1.0 amp full deflection. Ga = 19.98 S has ~50.050 mΩ resistance. 19.98 S + 50 mV - 999 mA 1 mA 1.0 A Docsity.com Example: 10 Amp F.S. Ammeter Scale chosen for 10 amp full deflection. Ga = 199.98 S has ~5.0005 mΩ resistance. 199.98 S + 50 mV - 9.999 A 1 mA 10 A Docsity.com Example: Voltage Measurement Measured Voltage: 10045 8.9286 100400 1 100 10 oV V k Ω = =  Ω Ω + + Ω Ω  8.9286% 1 100% 0.794% 9.0 VError V   = − = −    Docsity.com Another Voltage Measurement (1/2) True Voltage: (If voltmeter removed) 1045 9 50o kV V V k Ω = = Ω 45 V 40 kΩ 10 kΩ + Vo - 10 kΩ volt- meter Docsity.com Another Voltage Measurement (2/2) Measured Voltage: 1045 5.0 1040 1 10 10 o kV V V kk k k Ω = =  Ω Ω + + Ω Ω  5.0% 1 100% 44.44% 9.0 VError V   = − = −    Docsity.com Another Current Measurement (1/2) True Current: (If ammeter replaced by short circuit) 255 1.0 125o mI A A m Ω = = Ω 5A 100 mΩ 25 mΩ 50 mΩ Ammeter Io Docsity.com Another Current Measurement (2/2) Measured Current: 255 0.7143 175o mI A A m Ω = = Ω 0.7143% 1 100% 28.57% 1.0 AError A   = − = −    Docsity.com Measuring Resistance • Indirect – Measure Voltage across Resistor – Measure Current through Resistor – Calculate Resistance (Inaccurate) • d’Arsonval Ohmmeter – Very Simple – Inaccurate • Wheatstone Bridge (Most Accurate) Docsity.com Wheatstone Bridge Vg Rg R1 R2 R3 Rx a b c d + Vab - I 1 I 2 I 3 I x I ab 2 3 1 x R RR R ⋅ = Vab= 0 and Iab= 0 Vad = Vbd I1 = I3 I2 = Ix R1I1=R2I2 R3I3=RxIx Docsity.com Example: Wheatstone Bridge 1 kV 100 Ω 150 Ω 300 Ω 450 Ω 900 Ω a b c d RqI 150 300 450 900 Ω Ω = Ω Ω I = 2 A Docsity.com