PHY2049 Current Circuits February 08 News Quiz Today

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!

H ot , H ot A closed circuit

Power in DC Circuit

Let’s add resistors …….

SERIES Resistors i i R 1 R 2 Series Combinations V 1 V 2 V

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? ? R 1, I 1 R 2, I 2 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 P 28. 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 Internal Resistance 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!

A Physical (Real) Battery Intern al Re sistan ce

Which is brighter?

Which is Brighter? ? ? Which is Brighter

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

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: rise -E +ir +i. R = 0 or E=ir + i. R

Circuit Reduction i=E/Req

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: rise -E +ir +i. R = 0 or E=ir + i. R

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 W 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 28. 24. (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=CE(1 -e-t/RC)

q=CE(1 -e-t/RC) and i=(CE/RC) et/RC

Discharging a Capacitor qinitial=CE BIG SURPRISE! (Q=CV) i i. R+q/C=0