Chapter 27: Circuits Introduction What are we going to talk about in chapter 28: What is an electromotive force ( E : emf)? What is the work done by an emf? What is an ideal emf? How does it differ from real emfs? What is Kirchhoff ’ s voltage law (KVL)? What is Kirchhoff ’ s current law (KCL)? Resistors connected: series and/ or parallel RC circuits, time constant:  = R C

An emf (ElectroMotive Force) device is a [charge pump] device that (unlike a capacitor) maintains a constant potential difference between a pair of terminals. Emfs do work on charges. 27-2: Pumping charges Examples: batteries, generators and solar cells.

27-3: Work, energy and emf There must be a source of energy in the emf device that moves positive charge carriers from the negative (low potential and potential energy) terminal to the positive (high potential and potential energy) terminal. This source may be chemical, mechanical, thermal or electromagnetic in nature. The internal chemistry causes a net flow of positive charge carriers from the negative terminal to the positive terminal (i.e. in the direction of the emf arrow).

The emf ( E ) of a device is the work per unit charge that the device does in moving charge from its LP terminal to its HP terminal. E = dW/dq [ E ] = volt What is an ideal emf? How does it differ from real emfs? As an example for emfs and their function, let ’ s look at figure 28-2.

We can analyze using the energy method: dW = E dq = E i dt == i 2 R dt i = E /R 27-4:Calculating the current in a single-loop circuit:

We can analyze using the potential method: Using Kirchhoff ’ s voltage law. KVL: The algebraic sum of the changes in potential encountered in a complete traversal of any loop of a circuit must be zero. i = E /R

Note: What happens when you cross a resistor in the same (or opposite) direction as the current? [resistance rule] What happens when you cross an emf in the same (or opposite) direction as the current? [emf rule] Checkpoint 1

Internal resistance: In the case of a real battery, there is internal resistance. E – i r - i R = 0 There is a difference, for real batteries, between emf and terminal voltage. 27-5: Other single loop circuits:

Resistance in series: R eq =  R i Resistances connected in series can be replaced with an equivalent resistance that has the same current and the same total potential difference as the actual resistances. Checkpoint 2

27-6: Potential differences: To find the potential difference between two points, apply resistance rule and emf rule in going from one point to the other.

When the battery is in “ normal ” mode: P = P emf – P r When the battery is recharging: P = P emf + P r Checkpoint 3 P = i V P emf = i E P r = i 2 r Power, potential and emf:

Resistance in parallel: (R eq ) -1 =  (R i ) -1 Resistances connected in parallel can be replaced with an equivalent resistance that has the same potential difference and the same total current as the actual resistances. 27-7: Multi-loop circuits: Kirchhoff ’ s current law (KCL):  i in =  i out For two resistances in parallel: R eq = R 1 R 2 /(R 1 + R 2 ) Checkpoint 4

You need to solve a “ differential equation ” to find how the charge and current change with time. 27-9: RC circuits: Charging an RC circuit:  = R C I o = E /R Q = E C q(t) = Q (1-e -t/  ]) I(t) = I o exp -t/ 

Discharging an RC circuit: q(t) = Q exp -t/  I(t) = I o exp -t/ 