Physics IDirect Current Electricity

DC

Assignment

• P&P22:1,3,10,13-16,32,62-64

• P&P23:4,7,11,16,55,57-59,64-67

• Circuit Practice:

• http://www.picra.net/csk/physics/CircuitProblems.html

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, I V, Voltage in volts, v

I, current in amperes, a

E = IR or V = IRE, 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

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 - 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!!

Cardinal Rules - Series

• E = Vt = V1 + V2 + V3

•I t = I1 = I2 = I3•Rt = R1 + R2 + R3

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

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

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

1. Controls amount of current flow

2. Controls voltage across a load

3. Protects expensive instruments

Rules for Meter Usage

A. Handle gently

B. Connect voltmeter in parallel

C. Connect ammeter in series

D. Polarity labels tell how to connect meters

E. Red (+) and Black (-)1. + should be wired directly or though other

components to the + terminal of the voltage source

Meter Rules Continued

F. When taking readings of unknown amounts, start at highest range or just tap

G. Know meter scales BEFORE closing a circuit so accurate readings can be taken quickly

H. Using tapping rule when first closing a circuit so accurate readings can be taken quickly

Meter rules, cont.

I. Have circuit approved before closing the circuit

J. Report trouble immediately

K. AC & DC meters are NOT interchangeable (unless so designed)

L. Avoid overheating 1. Joule’s Law Q = I2 RT / J

2. Q I2

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 +

More practice at…

• http://www.picra.net/csk/physics/CircuitProblems.html

Other methods of determining resistance

• Nature of the Material• R = L/A is resistivity of a

conductor in cm• 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, Cu at 20.0oC = 1.72x10-6 cm)

• R = L = 1.72x10-6 cm) (2000cm)• A (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. Its operation is similar to the original potentiometer except that in potentiometer circuits the meter used is a sensitive galvanometer.

• • • Wheatstone's bridge circuit diagram.• In the circuit at right, Rx is the unknown resistance to be measured; R1, R2 and R3

are resistors of known resistance and the resistance of 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. R2 is varied until this condition is reached. The current direction indicates if R2 is too high or too low.

• Detecting zero current can be done to extremely high accuracy (see Galvanometer). Therefore, if R1, R2 and R3 are known to high precision, then Rx can be measured to high precision. Very small changes in Rx disrupt the balance and are readily detected.

• If the bridge is balanced, which means that the current through the galvanometer Rg is equal to zero, the equivalent resistance of the circuit between the source voltage terminals is:

• R1 + R2 in parallel with R3 + Rx• http://en.wikipedia.org/wiki/Wheatstone_bridge

•

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