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 = 30VSo 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 areB] 2 & 3 areC] 1 & 4 areD] both B&CE] 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 resistorin 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 determinewithout a lengthy calculation

What is I1 ??

A] 0 A

B] 1 A

C] 2 A

D] 10 A

E] cannot determinewithout 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 theLOWER 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 theUPPER 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 theLOWER 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. (That would require a sudden jump in the charge Q)

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 currentThrough the battery?

A] 0 AB] 0.5 AC] 1 AD] 2 A

A long time after closing the switch, what is the currentThrough the battery?

A] 0 AB] 0.5 AC] 1 AD] 2 A

A long time after closing the switch, what is the potential dropacross the capacitor?

A] 0 VB] 10 VC] 20 VD] 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 AB] 0.5 A downwardC] 0.5 A upwardD] 1 A downwardE] 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 exponentialThe 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

A] 0

B] Ienc times a positive constant

C] -Ienc times a positive constant

€

vB ⋅d

v A ∫ = ?

€

vE ⋅d

v A ∫ = qenc /ε0

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