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QUESTIONS? PLEASE ASK!
From last time

Temperature dependence
of resistivity/resistance
  o [1  (T  To )] R  R o [1  (T  To )]

Electrical Energy:
Q

V  I V
t

V 2
 I R 
R
2
Superconductors

Remarkable materials
Example Problem

17.40 A certain toaster has a
heating element made of
Nichrome resistance wire. When
the toaster (at 20°C) is first
connected to 120 V source, the
initial current is 1.80 A, but the
current decreases when the
element heats up. When the
toaster reaches it final
temperature, the current is 1.53
A. (a) Find the power the toaster
produces at its final
temperature. (b) What is the
final temperature?
Solution to 17.40
Chapter 18
Direct Current Circuits
emf

emf maintains the current in a closed
circuit





Any device that increases the potential
energy of charges circulating in circuits;
e.g., batteries and generators
SI units are Volts
The emf is the work done per unit charge
Real batteries have small internal
resistance
Therefore, the terminal voltage is not
equal to the emf
Internal Resistance

internal resistance  r

Terminal voltage: ΔV = Vb-Va

ΔV = ε – Ir



This is the voltage drop that the
circuit ‘sees’
For the entire circuit, ε = IR + Ir

load resistance R

When R >> r, r can be ignored

Generally assumed in problems
Power: I e = I2 R + I2 r

When R >> r, most of the power
delivered by the battery is
transferred to the load resistor
Resistors in Series

Current is the same in R1 and R2




Conservation of charge
ΔV = ΔV1 + ΔV2
= IR1 + IR2
= I (R1+R2)
= I Req
General: Req = R1 + R2 + R3 + …
The equivalent resistance has
the effect on the circuit as the
original combination of resistors
Equivalent Resistance –
Series: An Example

Four resistors are replaced with their
equivalent resistance
Resistors in Parallel

Equivalent resistance replaces the two original
resistances
Equivalent Resistance –
Parallel



Current splits at upper
junction: I = I1 + I2 + I3
Write in terms of voltage
drop DV DV DV DV
=
+
+
Req R1 R2 R3
Equivalent Resistance
1
1
1
1
=
+
+
+…
R eq R1 R 2 R 3

The equivalent resistance is
always less than the
smallest resistor in the
group!
Example Problem 18.8
(a) Calculate the equivalent resistance
of the 10 Ω and 5 Ω resistors. (b)
Calculate the combined equivalent
resistance of the 10 Ω, 5 Ω, and 4 Ω
resistors. (c) Calculate the equivalent
resistance found in part b and the
parallel 3 Ω resistor. (d) Combine the
equivalent resistance from part c and
the 2 Ω resistor. (e) Calculate the total
current in the circuit. (f) What is the
voltage drop across the 2 Ω resistor?
(g) Subtracting the result of part f from
the battery voltage, find the voltage
across the 3 Ω resistor. (h) Calculate
the current in the 3 Ω resistor.
Solution to 18.8 (I)
Solution to 18.8 (II)
Example Problem 18.13
Find the current in the 12 Ω resistor.
Solution to 18.13 (I)
Solution to 18.13 (II)