Direct Current Electricity DC Physics I Direct Current Electricity DC

Assignment Ch34: 696/1,2,6-10,12,15,16,19,20,26-28 AND 697/29,30,59,60,66-70,73 AND Benchmark Review on 701A Ch35: Circuit Practice: 714/1,3,6,7,9,13,16-18 AND 716/22,24,39,40,52,55 AND Benchmark Review on 719A

1. Current Electricity – charges in motion A. Circuit – a continuous loop through which electricity can flow. It must contain 1. Energy source – battery, generator 2. Conductor – copper wire is common 3. Load – device(s) that converts electrical energy to other useful forms of energy

B. Circuit Types 1. Parallel Circuit - more than 1 path is provided for current to flow 2. Series Circuit - one path for current to flow

Schematic Symbols

Ohm’s Law R = V R, Resistance in Ohms, W I V, Voltage in volts, v I, current in amperes, a E = IR or V = IR E, voltage in volts, for the overall circuit V, potential drop across a section of a circuit

2. Cardinal rules for Resistors A. Voltage or Electromotive Force (across battery) is equal in parallel Vbattery = V1 = V2 = V3 = ... B. Current is additive in parallel Itotal = I1 + I2 + I3 + ... Kirchhoff’s 1st Law or Junction Rule - the total current entering a junction must be equal to the total current leaving the junction.

C. Resistance in Parallel

Equivalent Resistance

Cardinal Rule for Req This is the concept of equivalent resistance. The equivalent resistance of a circuit is the amount of resistance which a single resistor would need in order to equal the overall effect of the collection of resistors which are present in the circuit. For parallel circuits, the mathematical formula for computing the equivalent resistance (Req) is 1 / Req = 1 / R1 + 1 / R2 + 1 / R3 + ...

Series Circuit – only 1 path is provided for current

Voltage is additive in series Vbattery = V1 + V2 + V3 + ... Kirchoff’s 2nd Law or the Loop Rule: The algebraic sum of the potential differences that occur around a complete circuit is equal to zero. E - (V1 + V2 + V3 + …) = 0

Ibattery = I1 = I2 = I3 = V / Req Current in series Ibattery = I1 = I2 = I3 = ... Ibattery = I1 = I2 = I3 =   V / Req

Which leads us to Rt = R1 + R2 + R3 + ...  since the current is the same

Cardinal Rules - Series E = Vt = V1 + V2 + V3 I t = I1 = I2 = I3 Rt = R1 + R2 + R3 1/Ct = 1/C1 + 1/C2 + 1/C3 Or: Ct = 1 1/C1 + 1/C2 + 1/C3

Cardinal rules - Parallel E = Vt = V1 = V2 = V3 = … Voltages are equal in parallel It = I1 + I2 + I3 + … Current is additive in parallel 1/Rt = 1/R1 + 1/R2 + 1/R3 Or: Rt = 1 1/R1 + 1/R2 + 1/R3 Or As more resistance is added, the resistance goes DOWN!! And the current goes UP! Circuit breaker opens

Joule’s Law E = I2Rt E, quantity of energy in joules I, current in amps R, resistance in ohms t, time in sec E proportional to I2

Power, rate of doing work P = IV P = I2 R Energy, E = Power x time, j/s x s = joule P, Power: watt = joule/sec I, Current: ampere = coulomb/sec V, Voltage: volt = joule/coulomb R, Resistance: ohm E, Energy: joule

Sample Problem 22/1 The current through a light bulb connected across the terminals of a 125 v outlet is 0.50 a. at what rate does the bulb convert electric energy to light? P = IV P = (0.50 a)(125 v) P = 63 w

Problem Applications

15. continued

On the prior slide, simplification shown in the diagrams gives way to what is needed to be done mathematically using the Cardinal Rules: Series: V is +, I is =, R is + Parallel: V is =, I is +, R is 1/R +

Meters Voltmeter – measure difference in potential between 2 points in a circuit ALWAYS connected in parallel with the part of the circuit to be measured (acts as a load) http://www.facstaff.bucknell.edu/mastascu/elessonshtml/Measurements/MeasVolt.html

Rules for Meter Usage Handle gently Connect voltmeter in parallel Connect ammeter in series Polarity labels tell how to connect meters Red (+) and Black (-) + should be wired directly or though other components to the + terminal of the voltage source

Meter Rules Continued When taking readings of unknown amounts, start at highest range or just tap Know meter scales BEFORE closing a circuit so accurate readings can be taken quickly Using tapping rule when first closing a circuit so accurate readings can be taken quickly

Meter rules, cont. Have circuit approved before closing the circuit Report trouble immediately AC & DC meters are NOT interchangeable (unless so designed) Avoid overheating Joule’s Law Q = I2 RT / J Q a I2

Ammeter – measures current ALWAYS placed in series in a circuit Be sure current does not exceed range of meter (use rheostat or “tap” or set meter at highest range, if possible) The ammeter is placed in SERIES with one lead of a circuit. It must be placed around the correct way so the needle moves up-scale.  http://www.talkingelectronics.com/html/CctSymbolsE-Book-Web/CircuitSymbolsE-Book-Web.html

Galvanometer Used to measure weak electric currents only

Rheostat - variable resistor Controls amount of current flow Controls voltage across a load Protects expensive instruments

Other methods of determining resistance Nature of the Material R = rL/A r is resistivity of a conductor in Wcm L is length of conductor, cm A is cross sectional area of conductor, cm2 Wheatstone Bridge

Problem sample What is the resistance of Copper wire 20. m long, 0.81 mm diameter at 20.0oC? (Resistivity, rCu at 20.0oC = 1.72x10-6 Wcm) R = r L = 1.72x10-6 Wcm) (2000cm) A p(8.1x10-2cm)2 4 R =

A Wheatstone bridge is a measuring instrument invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843. It is used to measure an unknown electrical resistance by balancing two legs of a bridge circuit, one leg of which includes the unknown component. http://en.wikipedia.org/wiki/Wheatstone_bridge

R1 + R2 in parallel with R3 + Rx Rx is unknown R1,R2, & R3 are known. R2 is adjustable. . If the ratio of the two resistances in the known leg (R2 / R1) is equal to the ratio of the two in the unknown leg (Rx / R3), then the voltage between the two midpoints will be zero and no current will flow between the midpoints. R1 + R2 in parallel with R3 + Rx

members.shaw.ca/roma/res_cap.html

Sources http://www.glenbrook.k12.il.us/gbssci/phys/Class/circuits/u9l4a.html http://www.ieee.org/portal/cms_docs_iportals/iportals/education/preuniversity/tispt/pdf/lessons/serpar.pdf