# بسم الله الرحمن الرحيم 19-11-2014 FCI.

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بسم الله الرحمن الرحيم FCI

Chapter 3 (CH 28) Direct Current Circuits: 3-1 EMF
3-2 Resistance in series and parallel . 3-3 Kirchhoff’s Rules 3-4 RC circuit 3-5 Electrical instruments - Weston bridge -Potentiometer FCI

Objectives: Defined some circuits in which resistors can be combined using simple rules. Understand the analysis of more complicated circuits is simplified using two rules known as Kirchhoff’s rules. Describe electrical meters for measuring current and potential difference FCI

1- Sources of emf The source that maintains the current in a closed circuit is called a source of emf Any devices that increase the potential energy of charges circulating in circuits are sources of emf Examples include batteries and generators SI units are Volts The emf is the work done per unit charge FCI

emf and Internal Resistance
A real battery has some internal resistance “r” Therefore, the terminal voltage is not equal to the emf FCI

The schematic shows the internal resistance, r The terminal voltage is ΔV = Vb-Va ΔV = ε – Ir For the entire circuit, ε = IR + Ir FCI

Now imagine moving through the battery from a to b and measuring the electric potential at various locations. As we pass from the negative terminal to the positive terminal, the potential increases by an amount Ɛ. As we move through the resistance r, the potential decreases by an amount Ir. Constant potential from b to c. As we move through the resistance R, the potential decreases by an amount IR FCI

Internal Resistance and emf, cont
ε is equal to the terminal voltage when the current is zero Also called the open-circuit voltage R is called the load resistance The current depends on both the resistance external to the battery and the internal resistance FCI

Internal Resistance and emf, final
When R >> r, r can be ignored Generally assumed in problems Power relationship I e = I2 R + I2 r When R >> r, most of the power delivered by the battery is transferred to the load resistor FCI

Quiz 1 In order to maximize the percentage of the power that is delivered from a battery to a device, the internal resistance of the battery should be: (a) as low as possible (b) as high as possible (c) The percentage does not depend on the internal resistance. FCI

Example 1: A battery has an emf of 12.0 V and an internal resistance of 0.05 Ω. Its terminals are connected to a load resistance of 3.00 Ω. (A) Find the current in the circuit and the terminal voltage of the battery. (B) Calculate the power delivered to the load resistor, the power delivered to the internal resistance of the battery, and the power delivered by the battery. FCI

2-Resistors in Series When two or more resistors are connected end-to-end, they are said to be in series The current is the same in all resistors because any charge that flows through one resistor flows through the other The sum of the potential differences across the resistors is equal to the total potential difference across the combination FCI

Resistors in Series, cont
Potentials add ΔV = IR1 + IR2 = I (R1+R2) Consequence of Conservation of Energy The equivalent resistance has the effect on the circuit as the original combination of resistors FCI

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 resistors FCI

Equivalent Resistance – Series: An Example
Four resistors are replaced with their equivalent resistance FCI

Quiz 2: With the switch in the circuit of Fig. A closed, there is no current in R2, because the current has an alternate zero-resistance path through the switch. There is current in R1 and this current is measured with the ammeter, at the right side of the circuit. If the switch is opened (Fig. B), there is current in R2 . What happens to the reading on the ammeter when the switch is opened? (a) the reading goes up; (b) the reading goes down; (c) the reading does not change. FCI

(b). When the switch is opened, resistors R1 and R2 are in series, so that the total circuit resistance is larger than when the switch was closed. As a result, the current decreases. FCI

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 FCI

Equivalent Resistance – Parallel, Example:
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 FCI

Equivalent Resistance – Parallel
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 FCI

Problem-Solving Strategy, 1
Combine all resistors in series They carry the same current The potential differences across them are not the same The resistors add directly to give the equivalent resistance of the series combination: Req = R1 + R2 + … FCI

Problem-Solving Strategy, 2
Combine all resistors in parallel The potential differences across them are the same The currents through them are not the same The equivalent resistance of a parallel combination is found through reciprocal addition: FCI

Problem-Solving Strategy, 3
A complicated circuit consisting of several resistors and batteries can often be reduced to a simple circuit with only one resistor Replace any resistors in series or in parallel using steps 1 or 2. Sketch the new circuit after these changes have been made Continue to replace any series or parallel combinations Continue until one equivalent resistance is found FCI

Problem-Solving Strategy, 4
If the current in or the potential difference across a resistor in the complicated circuit is to be identified, start with the final circuit found in step 3 and gradually work back through the circuits Use ΔV = I R and the procedures in steps 1 and 2 FCI

Equivalent Resistance
– Complex Circuit FCI

Quiz 3: With the switch in the circuit of Fig. A open, there is no current in R2. There is current in R1 and this current is measured with the ammeter at the right side of the circuit. If the switch is closed Fig.B, there is current in R2. What happens to the reading on the ammeter when the switch is closed? (a) the reading goes up; (b) the reading goes down; (c) the reading does not change. FCI

(a). When the switch is closed, resistors R1 and R2 are
in parallel, so that the total circuit resistance is smaller than when the switch was open. As a result, the current increases. FCI

I1 = I2 + I3 From Conservation of Charge Diagram b shows a mechanical analog FCI

Setting Up Kirchhoff’s Rules
Assign symbols and directions to the currents in all branches of the circuit If a direction is chosen incorrectly, the resulting answer will be negative, but the magnitude will be correct When applying the loop rule, choose a direction for transversing the loop Record voltage drops and rises as they occur FCI

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 +IR FCI

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 +ε In (d), the source of emf is transversed in the direction opposite of the emf (from + to -), the change in the electric potential is -ε FCI

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 FCI

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 FCI

Example: (A) Find the current in the circuit.
starting at a, we see that a b represents a potential difference of + Ɛ1 b  c represents a potential difference of -IR1, c  d represents a potential difference of - Ɛ2, and d  a represents a potential difference of -IR2 FCI

The negative sign for I indicates that the direction of the current is opposite the assumed direction. (B) What power is delivered to each resistor? What power is delivered by the 12-V battery? FCI

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