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Week5_2 Drexel PHYS 102
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  • Title: Week5_2
  • Type: Notes
  • School: Drexel
  • Course: PHYS 102
  • Term: Spring

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A emf source of emf (electromotive force) is an entity that maintains the constant voltage of a circuit The emf source supplies energy, it does not apply a force, to the circuit The battery will normally be the source of energy in the circuit Could also use generators Sample Circuit We consider the wires to have no resistance The positive terminal of the battery is at a higher potential than the negative terminal There is also an internal resistance in the battery Internal Battery Resistance If the internal resistance is zero, the terminal voltage equals the emf In a real battery, there is internal resistance, r The terminal voltage, V = - Ir emf, cont The emf is equivalent to the open-circuit voltage This is the terminal voltage when no current is in the circuit This is the voltage labeled on the battery The actual potential difference between the terminals of the battery depends on the current in the circuit Load Resistance The terminal voltage also equals the voltage across the external resistance This external resistor is called the load resistance In the previous circuit, the load resistance is the external resistor In general, the load resistance could be any electrical device Power The total power output of the battery is P = IV =I This power is delivered to the external resistor (I2 R) and to the internal resistor (I2r) P = I = I2 R + I2 r The current depends on the internal and external resistances I= R+r Resistors in Series When two or more resistors are connected endto-end, they are said to be in series For a series combination of resistors, the currents are the same in all the resistors because the amount of charge that passes through one resistor must also pass through the other resistors in the same time interval The potential difference will divide among the resistors such that the sum of the potential differences across the resistors is equal to the total potential difference across the combination Resistors in Series, cont Potentials add V = IR1 + IR2 = I (R1+R2) Consequence of Conservation of Energy The equivalent resistance has the same effect on the circuit as the original combination of resistors Equivalent Resistance Series Req = R1 + R2 + R3 + ... The equivalent resistance of a series combination of resistors is the algebraic sum of the individual resistances and is always greater than any of the individual resistances If one device in the series circuit creates an open circuit, all devices are inoperative Equivalent Resistance Series An Example Two resistors are replaced with their equivalent resistance Resistors in Parallel The potential difference across each resistor is the same because each is connected directly across the battery terminals The current, I, that enters a point must be equal to the total current leaving that point I = I1 + I2 The currents are generally not the same Consequence of Conservation of Charge Equivalent Resistance Parallel Equivalent Resistance 1 1 1 1 = + + +K R eq R1 R 2 R 3 The inverse of the equivalent resistance of two or more resistors connected in parallel is the algebraic sum of the inverses of the individual resistance The equivalent is always less than the smallest resistor in the group Equivalent Resistance Parallel, Examples Equivalent resistance replaces the two original resistances Household circuits are wired so the electrical devices are connected in parallel Circuit breakers may be used in series with other circuit elements for safety purposes Resistors in Parallel, Final In parallel, each device operates independently of the others so that if one is switched off, the others remain on In parallel, all of the devices operate on the same voltage The current takes all the paths The lower resistance will have higher currents Even very high resistances will have some current Circuit Reduction A circuit consisting of resistors can often be reduced to a simple circuit containing only one resistor Examine the original circuit and replace any resistors in series their with equivalents and any resistors in parallel with their equivalents Sketch the new circuit Examine it and replace any new series or parallel combinations with their equivalents Continue until a single equivalent resistance is found Circuit Reduction Example The 8.0 and 4.0 resistors are in series and can be replaced with their equivalent, 12.0 The 6.0 and 3.0 resistors are in parallel and can be replaced with their equivalent, 2.0 These equivalent resistances are in series and can be replaced with their equivalent resistance, 14.0 Kirchhoff's Rules There are ways in which resistors can be connected so that the circuits formed cannot be reduced to a single equivalent resistor Two rules, called Kirchhoff's Rules, can be used instead Statement of Kirchhoff's Rules Junction Rule At any junction, the sum of the currents must equal zero A statement of Conservation of Charge Loop Rule The sum of the potential differences across all the elements around any closed circuit loop must be zero A statement of Conservation of Energy Mathematical Statement of Kirchhoff's Rules Junction Rule: Iin = Iout Loop Rule: closed loop V = 0 More About the Junction Rule I1 - I2 - I3 = 0 Use +I for currents entering a junction Use I for currents leaving a junction From Conservation of Charge Diagram b shows a mechanical analog More About the Loop Rule Traveling around the loop from a to b In a, the resistor is transversed in the direction of the current, the potential across the resistor is IR In b, the resistor is transversed in the direction opposite of the current, the potential across the resistor is is +IR Loop Rule, final In c, the source of emf is transversed in the direction of the emf (from to +), the change in the electric potential is + In d, the source of emf is transversed in the direction opposite of the emf (from + to -), the change in the electric potential is - Junction Equations from Kirchhoff's Rules Use the junction rule as often as needed, so long as, each time you write an equation, you include in it a current that has not been used in a previous junction rule equation In general, the number of times the junction rule can be used is one fewer than the number of junction points in the circuit Loop Equations from Kirchhoff's Rules The loop rule can be used as often as needed so long as a new circuit element (resistor or battery) or a new current appears in each new equation You need as many independent equations as you have unknowns Kirchhoff's Rules' Equations, final In order to solve a particular circuit problem, the number of independent equations you need to obtain from the two rules equals the number of unknown currents Problem-Solving Hints Kirchhoff's Rules Conceptualize Study the circuit diagram Identify all the elements in the circuit Identify the polarity of all the batteries and imagine the directions in which the current would exist through the batteries Categorize Determine if the circuit can be reduced by combining series and parallel resistors If not, continue with the application of Kirchhoff's rules Problem-Solving Hints Kirchhoff's Rules, cont Analyze Draw the circuit diagram and assign labels and symbols to all known and unknown quantities. Assign directions to the currents The direction is arbitrary, but you must adhere to the assigned directions when applying Kirchhoff's Rules Apply the junction rule to any junction in the circuit that provides new relationships among the various currents Problem-Solving Hints, cont Analyze, cont Apply the loop rule to as many loops as are needed to solve for the unknowns To apply the loop rule, you must choose a direction to travel around the loop and correctly identify the potential difference as you cross various elements Solve the equations simultaneously for the unknown quantities If a current turns out to be negative, the magnitude will be correct and the direction is opposite to that which you assigned Finalize Check your answers for consistency

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Path: American University of Sharjah >> MCE >> 240 Spring, 2008
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Path: American University of Sharjah >> MCE >> 240 Spring, 2008
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Path: American University of Sharjah >> MECHANICAL >> 223,224,22 Spring, 2008
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Path: American University of Sharjah >> MECHANICAL >> 223,224,22 Spring, 2008
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Path: American University of Sharjah >> MECHANICAL >> 223,224,22 Spring, 2008
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Path: American University of Sharjah >> MECHANICAL >> 223,224,22 Spring, 2008
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Path: American University of Sharjah >> ARA >> 101,102 Spring, 2008
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Path: American University of Sharjah >> MECHANICAL >> 223,224,22 Spring, 2008
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Path: American University of Sharjah >> MECHANICAL >> 223,224,22 Spring, 2008
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Path: American University of Sharjah >> MECHANICAL >> 223,224,22 Spring, 2008
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Path: American University of Sharjah >> MECHANICAL >> 223,224,22 Spring, 2008
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Path: American University of Sharjah >> MCE >> 240 Spring, 2008
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Path: American University of Sharjah >> MECHANICAL >> 223,224,22 Spring, 2008
Description: MCE 230 Materials Science Gagan Gururaj ID: 8526 Email: b00008526@aus.ac.ae Instructor: Dr. Hany El-Kadi Date due: 14/12/03 Problems: Ch.4 4.4 4.11 4.18 4.23 4.34 Ch.5 5.3 5.6 5.11 5.25 ...
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Path: American University of Sharjah >> MECHANICAL >> 223,224,22 Spring, 2008
Description: Abstract: Three samples of unpolished aluminum and three samples of unpolished copper were used in the fatigue test. Under an applied load of 80N, the first sample of aluminum fractured after 13892 load cycles. Similarly, the second sample of aluminu...
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Path: American University of Sharjah >> MECHANICAL >> 223,224,22 Spring, 2008
Description: Stress (Pa) Primary parallel Secondary parallel Perpendicular Strain Stress Strain stress Strain Stress 0 6.05E+01 0 492.917 0 5803.364 0.000209 8.94E+04 0.000413 91217.01 6.26E-05 95780.96 0.000417 1.78E+05 0.000832 223763 0.000108 196940.9 0.00062...
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Path: American University of Sharjah >> ARA >> 101,102 Spring, 2008
Description: Na i Meaning \"contradicting poems, flytings\", pl. of na a (from the verb na a a \"to destroy, undo, rebut, oppose\"), synonymous with mun a t (from the verbal form III n a a): a form of poetic duelling in which tribal or personal insults are exchange...
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Path: American University of Sharjah >> ARA >> 101,102 Spring, 2008
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ARA 101 Essay Questions [1]
Path: American University of Sharjah >> ARA >> 101,102 Spring, 2008
Description: AMERICAN UNIVESITY OF SHARJAH COLLEGE OF ARTS AND SCIENCES Department of Arabic Studies ARA 101 Readings in Arabic Heritage Essay Questions for Fall 2007 To be submitted by 16.00 on the 5th of December 2007. The essays should be submitted in soft co...
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Path: American University of Sharjah >> ARA >> 101,102 Spring, 2008
Description: ARA 101 E Readings in Arabic Heritage (English Sections) Dr. Gavin Picken Office: NAB 222 Office Tel: ext. 2873 Office Hours: Sunday 11-12, Monday 11-12, Tuesday 3-4 and Wednesday 3-4. E-mail: gpicken@aus.edu B. Sc. Biological Sciences University ...
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Path: American University of Sharjah >> ARA >> 101,102 Spring, 2008
Description: - al b. al- alt, who died probably before 92/710. He belonged to the great tribe of the lib [q.v.] of northern Syria, which remained entirely Christian, of the Monophysite persuasion. By his mother Layla he was connected to another Christian tribe...
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Path: American University of Sharjah >> ARA >> 101,102 Spring, 2008
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Path: American University of Sharjah >> ARA >> 101,102 Spring, 2008
Description: al- Farazda \"the lump of dough\", properly Tammm b. lib (Ab Firs), famous Arab satirist and panegyrist, died at Ba ra about 110/728 or 112/730. Born in Yamma (Eastern Arabia) on a date which is uncertain (probably after 20/640), this poet i, of the Dr...
ḤassÄn b. Thabit EI [1]
Path: American University of Sharjah >> ARA >> 101,102 Spring, 2008
Description: bit - ir b. arm Of the tribe of rib (later Medna), traditionally known as the \"poet laureate\" of the Prophet, is more correctly the most prominent of several poets who were associated with the rise of Islam , and one who already had an establis...
Ḳaṣīda EI [1]
Path: American University of Sharjah >> ARA >> 101,102 Spring, 2008
Description: a da 1. In Arabic. a da collective a d is the name given in Arabic to some poems of a certain length. It is derived from the root a ada, \"to aim at\", for the primitive a da was intended to eulogize the tribe of the poet and denigrate the opposi...
Ḳabīla EI [1]
Path: American University of Sharjah >> ARA >> 101,102 Spring, 2008
Description: abla Denotes a large agnatic group, the members of which claim to be descended from one common ancestor; this word is generally understood in the sense of tribe. It derives from the Arabic root -b-l, of which the form bala signifies to meet, to be...

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