Transcript 27-3: Work, energy and emf

Chapter 27: Circuits
Introduction
What are we going to talk about in chapter 28:
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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)?
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What is Kirchhoff’s current law (KCL)?
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Resistors connected: series and/ or parallel
•
RC circuits, time constant: t = R C
27-2: Pumping charges
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.
Examples: batteries, generators and solar cells.
27-3: Work, energy and emf
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).
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 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.
27-4:Calculating the current in a single-loop circuit:
We can analyze using the energy method:
dW = E dq = E i dt == i2 R dt
i = E /R
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
27-5: Other single loop circuits:
Internal resistance: In the case of a real battery, there is internal
resistance.
E–ir-iR=0
There is a difference, for real batteries,
between emf and terminal voltage.
Resistance in series:
Req = S Ri
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.
Power, potential and emf:
When the battery is in “normal” mode:
P = Pemf – Pr
When the battery is recharging:
P = Pemf + Pr
P=iV
Pemf = i E
Pr = i2 r
Checkpoint 3
27-7: Multi-loop circuits:
Kirchhoff’s current law (KCL):
S iin = S iout
Resistance in parallel:
(Req)-1 = S (Ri)-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.
For two resistances in parallel:
Req = R1 R2 /(R1 + R2)
Checkpoint 4
27-9: RC circuits:
You need to solve a “differential equation” to find how the charge
and current change with time.
Charging an RC circuit:
t=RC
Io = E /R
Q=EC
q(t) = Q (1-e-t/t])
I(t) = Io exp-t/t
Discharging an RC circuit:
q(t) = Q exp-t/t
I(t) = Io exp-t/t