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When two resistors are in parallel, the current through
each is inversely proportional to R.
That’s because V=IR and, IN PARALLEL, all V’s are
the same.
What FRACTION OF total CURRENT
flows through R?
A] 1/3
B] 2/3
C] 1/4
D] 3/4
3/4 of the current flows through R.
1/4 of the current flows through 3R.
Now, recalling that P=I2R = V2/R
If the 3R is three light bulbs, and the R is one
light bulb: what is the ratio
of the power dissipated in the bulb on the left
To
the power dissipated in each of the bulbs on
the right?
A] every bulb dissipates equal power
B] 1:3 (each bulb on right is brighter than bulb
on left)
C] 3:1
D] 9:1
When resistors are IN SERIES, each resistor has a voltage drop
in proportion to R.
What is the voltage drop through the 20 ohm R?
2 Ways to think about this:
1: R ef = 10+20+30 = 60 ohm, so
I = 30 V/60 ohms = 0.5 A
V=IR gives 0.5 A x 20 ohm = 10V
2: 20 ohms is 1/3 of total R (60 ohms),
so it must have 1/3 of total V = 10 V.
USE V=IR to find potential as you walk around a circuit.
Set V=0 at the negative side of a battery (usually.)
In this problem, find V at the upper junction = 50V - IR = 30V
So there is 30V across the parallel resistors.
The 20 ohm resistor will have current
I = 30V/20 ohm = 1.5 A.
So 0.5 A must flow through R.
Unknown R = 30V/0.5 A = 60 ohms.
You have to look carefully to see what is in parallel and in series.
Are any resistors in parallel?
A] 4 & 5 are
B] 2 & 3 are
C] 1 & 4 are
D] both B&C
E] none are in parallel
We redraw the circuit, replacing the parallel resistors with Refs
We see that R5 is now in parallel with the 2 series Refs.
The total Ref = R/2 = 10 ohms. So I= 1 A and I5 = 0.5 A.
What is the unknown current, in terms of the given I’s ?
A] I1
B] I2
C] -I2
D] I1 + I2
Currents go through batteries!!!!
What is the downward current through the 5 ohm resistor
in terms of the given I’s ?
A] I1
B] I2
C] -I2
D] I1 + I2
E] I1 - I2
What is the change in voltage in going from A to B?
A] + 10 V
B] - 10 V
C] 0 V
D] cannot determine
without lengthy
calculation
What is the change in voltage in going from A to C?
A] + 10 V
B] - 10 V
C] 0 V
D] cannot determine
without lengthy
calculation
How much current flows through the 10 ohm resistor?
A] 0 A
B] 1 A
C] 2 A
D] 10 A
E] cannot determine
without a lengthy
calculation
What is I1 ??
A] 0 A
B] 1 A
C] 2 A
D] 10 A
E] cannot determine
without a lengthy
calculation
“Ground”
Some circuit diagrams show a connection to “ground”.
Ground is essentially the ground. Usually, we call ground 0V.
In some electrical equipment, the metal case is wire to ground, a
third wire. If there is a “short” inside where a high potential wire
touches the case, a LOT of current flows to ground and throws a
fuse or circuit breaker.
Without the ground connection, touching the case could cause
electrocution!
Capacitors in DC Circuits
The voltage across a capacitor is proportional to the charge Q.
It takes time for charge to be added or removed.
So the voltage across a capacitor CANNOT change suddenly.
If we throw a switch that charges the capacitor:
• at short times, the capacitor looks like a wire (no potential drop)
(we call this a short, or short circuit)
• at long times, no current flows through the capacitor. This is
because we are at “steady state”, so the capacitor voltage must
stay constant, and Q must stay constant. The capacitor looks like a
broken wire.
(we call this an open circuit.)
Immediately after closing the switch, what is the current through the
LOWER 10 ohm resistor?
A] 0
B] 0.5 A
C] 1 A
D] 2 A
Immediately after closing the switch, what is the current through the
UPPER 10 ohm resistor?
A] 0
B] 0.5 A
C] 1 A
D] 2 A
A LONG TIME after closing the switch, what is the current through the
LOWER 10 ohm resistor?
A] 0
B] 0.5 A
C] 1 A
D] 2 A
AFTER THE SWITCH HAS BEEN CLOSED FOR A LONG TIME,
IT IS OPENED. WHAT IS THE CURRENT IN THE LOWER
RESISTOR, RIGHT AFTER OPENING THE SWITCH?
A] 0
B] 0.5 A
C] 1 A
D] 2 A
AFTER THE SWITCH HAS BEEN CLOSED FOR A LONG TIME,
IT IS OPENED. WHAT IS THE CURRENT IN THE UPPER
RESISTOR, RIGHT AFTER OPENING THE SWITCH?
A] 0
B] 0.5 A
C] 1 A
D] 2 A
Capacitors & Switches
The voltage on a cap cannot change suddenly.
would require a sudden jump in the charge Q)
(That
If a switch is opened, current through the switch = 0, and
there is no current anywhere on that branch or loop.
Let’s practice more:
Immediately after closing the switch, what is the current
Through the battery?
A] 0 A
B] 0.5 A
C] 1 A
D] 2 A
A long time after closing the switch, what is the current
Through the battery?
A] 0 A
B] 0.5 A
C] 1 A
D] 2 A
A long time after closing the switch, what is the potential drop
across the capacitor?
A] 0 V
B] 10 V
C] 20 V
D] 40 V
After the switch has been closed a long time, it is opened.
What is the current through the resistor below the cap, RA?
A] 0 A
B] 0.5 A downward
C] 0.5 A upward
D] 1 A downward
E] 1 A upward
A charged capacitor will discharge over time, if the + and - sides
are connected. The current will flow from the + side, through the
connection, to the - side.
This may seem counterintuitive… don’t the + and - charges
attract across the cap gap?
Yes, but the mutual repulsion of the +’s and -’s is greater.
What is “a long time”? How fast
can we charge up a capacitor?
How fast can we discharge a capacitor?
Differential Equations!
Let’s use Q=CV and V=IR with the
Kirchoff voltage loop law to find an
equation for current vs. time.
First, though, what is the relationship
between Qcap and I?
I = dQ/dt
If curve C represents the current
into a capacitor, what curve could
represent the charge on that capacitor?
What curve could represent Vcap?
When charging or discharging a capacitor, the response is exponential
The time constant is RC, where R is the effective resistance that the
charge must go through in the charging/discharging process
1/e = 0.368…
If we discharge a capacitor, after time t = RC, 36.8% of the original
charge is left.
The ENERGY LEFT is 36.8% squared, or only 13.5%.
We can show that the energy lost from the capacitor is dissipated in the
resistor. Let’s do it!
MAGNETISM
•Known to the ancients
•Culturally & linguistically the fundamental force
A magnetic personality
Animal magnetism
Opposites attract
•Cures arthritis (well, probably not…)
Einstein showed that magnetism is simply electrical force as seen
from a “different perspective.”
It’s existence is a CONSEQUENCE of the way the spacetime fabric
of the universe is woven!
Currents cause magnetic fields. If we say that the
compass lines up along the field, then the field curls
around the wire. B field lines have no beginning or end!
Permanent magnets are just
collections of little current loops
In Jules Verne’s story “Journey to the Center of the Earth”,
some dudes travel deep inside the Earth. If this were
possible and they had a compass with them, what direction
would their N compass needle point?
A] toward the Earth’s northern geographic pole
B] toward the Earth’s southern geographic pole
C] it would have no preferred direction
Magnetic field lines curl around currents, forming closed loops.
As such, they have no beginning and no end.
•
What is the total flux of the magnetic field through any closed surface? Recall
that
 E  dA  q
enc
 B  dA  ?
A] 0

B] Ienc times a positive constant
C] -Ienc times a positive constant
/0
Note key differences with E fields:
NO force if v=0
NO force if v is parallel to B
Direction of force depends on direction of v (perp to v!)
Five + charges are
located as shown, moving
with velocity vectors
shown. A uniform B field
exists throughout all
space
Which does NOT feel a
magnetic force?
The speeds are all the same.
How does the mag force on
b compare to the mag force
on d?
a) They are the same
b) Force on d is larger by √2
c) Force on b is larger by √2
d) Force on d is larger by 2
e) Force on b is larger by 2
The speeds are all the same.
How does the mag force on
e compare to the mag force
on a?
a) They are the same
b) Force on a is larger by √2
c) Force on e is larger by √2
d) Force on a is larger by 2
e) Force on e is larger by 2
What is the direction of the
magnetic force on
positive charge d?
a) +y
b) -y
c) +xz (at 45° to +x & +z)
d) At 45° to -x & -z
e) +z