PHY-2049 Current & Circuits February ‘08

News Quiz Today Examination #2 is on Wednesday of next week (2/4/09) It covers potential, capacitors, resistors and any material covered through Monday on DC circuits. No review session on Wednesday – Exam Day!

A closed circuit Hot, Hot Hot

Power in DC Circuit

Let’s add resistors …….

Series Combinations R1 R2 ii V1 V2 V SERIES Resistors

The rod in the figure is made of two materials. The figure is not drawn to scale. Each conductor has a square cross section 3.00 mm on a side. The first material has a resistivity of 4.00 × 10–3 Ω · m and is 25.0 cm long, while the second material has a resistivity of 6.00 × 10–3 Ω · m and is 40.0 cm long. What is the resistance between the ends of the rod?

Parallel Combination?? R1, I1 R2, I2 V

What’s This??? In the figure, find the equivalent resistance between points (a) F and H and [2.5] (b) F and G. [3.13]

(a) Find the equivalent resistance between points a and b in Figure P28.6. (b) A potential difference of 34.0 V is applied between points a and b. Calculate the current in each resistor.

Power Source in a Circuit The ideal battery does work on charges moving them (inside) from a lower potential to one that is V higher.

A REAL Power Source is NOT an ideal battery V E or Emf is an idealized device that does an amount of work E to move a unit charge from one side to another. By the way …. this is called a circuit! Internal Resistance

A Physical (Real) Battery Internal Resistance

Which is brighter?

Which is Brighter Which is Brighter???

Back to Potential Represents a charge in space Change in potential as one circuits this complete circuit is ZERO!

Consider a “circuit”. This trip around the circuit is the same as a path through space. THE CHANGE IN POTENTIAL FROM “a” AROUND THE CIRCUIT AND BACK TO “a” is ZERO!!

To remember In a real circuit, we can neglect the resistance of the wires compared to the resistors. ▫We can therefore consider a wire in a circuit to be an equipotential – the change in potential over its length is slight compared to that in a resistor A resistor allows current to flow from a high potential to a lower potential. The energy needed to do this is supplied by the battery.

NEW LAWS PASSED BY THIS SESSION OF THE FLORIDUH LEGISLATURE. LOOP EQUATION ▫The sum of the voltage drops (or rises) as one completely travels through a circuit loop is zero. ▫Sometimes known as Kirchoff’s loop equation. NODE EQUATION ▫The sum of the currents entering (or leaving) a node in a circuit is ZERO

TWO resistors again i R 1 R 2 V 1 V 2 V

A single “real” resistor can be modeled as follows: R a b V position ADD ENOUGH RESISTORS, MAKING THEM SMALLER AND YOU MODEL A CONTINUOUS VOLTAGE DROP.

We start at a point in the circuit and travel around until we get back to where we started. If the potential rises … well it is a rise. If it falls it is a fall OR a negative rise. We can traverse the circuit adding each rise or drop in potential. The sum of all the rises around the loop is zero. A drop is a negative rise. The sum of all the drops around a circuit is zero. A rise is a negative drop. Your choice … rises or drops. But you must remain consistent.

Take a trip around this circuit. Consider voltage DROPS : - E +ir +iR = 0 or E =ir + iR rise

Circuit Reduction i= E /R eq

Reduction Computes i

Another Reduction Example PARALLEL

Battery A battery applies a potential difference between its terminals. Whatever else is connected (circuits, etc.), the potential between the points remains the same: the battery potential.

Take a trip around this circuit. Consider voltage DROPS : - E +ir +iR = 0 or E =ir + iR rise

Multiple Batteries

START by assuming a DIRECTION for each Current Let’s write the equations.

In the figure, all the resistors have a resistance of 4.0  and all the (ideal) batteries have an emf of 4.0 V. What is the current through resistor R?

Consider the circuit shown in the figure. Find (a) the current in the 20.0-Ω resistor and (b) the potential difference between points a and b.

Using Kirchhoff’s rules, (a) find the current in each resistor in Figure P (b) Find the potential difference between points c and f. Which point is at the higher potential?

The Unthinkable ….

RC Circuit Initially, no current through the circuit Close switch at (a) and current begins to flow until the capacitor is fully charged. If capacitor is charged and switch is switched to (b) discharge will follow.

Close the Switch I need to use E for E Note RC = (Volts/Amp)(Coul/Volt) = Coul/(Coul/sec) = (1/sec)

Really Close the Switch I need to use E for E Note RC = (Volts/Amp)(Coul/Volt) = Coul/(Coul/sec) = (1/sec)

This is a differential equation. To solve we need what is called a particular solution as well as a general solution. We often do this by creative “guessing” and then matching the guess to reality. You may or may not have studied this topic … but you WILL!

Time Constant

Result q=C E (1-e -t/RC )

q=C E (1-e -t/RC ) and i=(C E /RC) e - t/RC

Discharging a Capacitor q initial =C E BIG SURPRISE! (Q=CV) i iR+q/C=0