8. Electricity

Question 1

What is current?

Answer 1

I = Q / t

Current is the net movement of charge over time, measured in C / s, amperes (A).

Question 2

If current is the movement of charge, then what causes this movement of charge?

Answer 2

The change in electric potential between two areas (where electric potential is the scalar field of source charge(s)) causes the movement of charge. This is voltage.

Voltage is also referred to as the electromotive force (emf) when it causes current. If V = 0, no current occurs.

Question 3

What is resistance? What is Ohm’s law?

Answer 3

Resistance is an intrinsic property of any material.

R = V / I, which is measured in Ohms (Ω)

more common formula known as Ohms Law: V = IR

Question 4

What is the formula for resistance using a materials resistivity?

Answer 4

R = ρ L/A

ρ = materials intrinsic resistivity 
A = cross-sectional area

Question 5

How do you find the equivalent resistance of two resistors

a) in series
b) in parallel

Answer 5

In series, we simply add their resistances (R1 + R2)

In parallel, we use this formula.
R equivalent = R1 x R2 / R1 + R 2
This ONLY works with two resistors at a time.

You can add all of the reciprocals together too (1/R = 1/R1 + 1/R2 + etc) which allows you to do as many at a time as you want

Question 6

t or f, for a parallel circuit, the equivalent resistance is always less than the smallest resistance in the combination.

Answer 6

true

Question 7

Explain the positive and negative terminals of a battery in a circuit.

Answer 7

The longer line represents the terminal with higher electric potential (the positive terminal)
The shorter line represents the terminal with lower electric potential (the negative terminal).

electrons move from the negative terminal (lower φ) to the positive terminal (higher φ).

Question 8

T or f, the convention for defining current is the direction positive charges would move in a circuit.

Answer 8

true, thus, electrons move opposite conventional current.

So we say that the current is from the positive terminal to the negative terminal (even though its actually the opposite).

Question 9

If two resistors are in series, how do we find the voltage drop and current that occurs over both of them?

Answer 9

If V1 occurs over R1 and V2 occurs over R2, then the voltage drop that occurs over both resistors is just V1 + V2

Current through R1 must equal current through R2

Question 10

If two resistors are in parallel, how do we find the voltage drop and current that occurs over both of them?

Answer 10

current into the parallel combination must equal current out the parallel system. To find the total current over resistors R1 and R2 in parallel, we just get I1 + I2

Voltage is the same across each resistor in parallel

Question 11

Kirchhoff’s laws: explain the voltage rule and the current rule.

Answer 11

Voltage: for any circuit containing one battery, the voltage drop amongst all resistors must equal the voltage gain of that battery

Current: the total current through a parallel system is equal to the sum of the currents passing through each individual resistor in the system.

Question 12

Recall, Power = work / time. Resistors dissipate power in the form of heat. What is the formula for this?

What is the formula for the power provided by the battery?

Answer 12

Resistor dissipation: P = I^2 x R

Battery power: P = IV

the power provided by the battery is equal to the total power dissipated by all the resistors

Notice that these equations are actually equal since (V = IR). Since batteries don’t typically give resistance, we use P = IV

Question 13

How do you find the energy associated with a resistor?

Answer 13

Power = work / time

Power = energy / time

energy = power x time

This is also how you would find the work done by a resistor.

Question 14

What is internal resistance and terminal voltage?

Answer 14

All batteries have some internal resistance. The terminal voltage is the true voltage provided by the battery when that battery is providing the current.

if current is being supplied to a battery (i.e. charging) the terminal voltage is actually greater than the emf.

Question 15

How does an ammeter and voltmeter work?

Answer 15

ammeter - measures current across a resistor by connecting in series with that resistor

voltmeter - measures voltage across a resistor by connecting in parallel with that resistor.

Question 16

What is a capacitor? In general, how can you create one?

Answer 16

A capacitor is any pair of conductors that can hold equal and opposite charge. If we connect a capacitor | | to a battery, then…
electrons will leave the one conductor to move to the positive battery terminal (making this plate positive). Electrons will be repelled by the negative terminal and accumulate on the other plate (making it negative).

Current will continue to flow until the voltage between the two plates of the capacitor equals that of the battery.

Question 17

How do you find the charge on a capacitor (note that the charge is just the magnitude either of the two plates). What is capacitance (C)?

Answer 17

Q = CV, where C is the capacitance of a capacitor and V is the voltage between the plates.

C = e A / d
A - size of the plates
d - distance between plates
e - permittivity of free space (this just determines whether there is something between the plates or not)

Question 18

What is a Farad?

Answer 18

Farads are Coulombs per Volt, which is the unit for capacitance.
Q = CV

C = Q / V

Question 19

Can you use Q = CV to find capacitance?

Answer 19

NO, you must use C = e A / d in all cases. C only tells us how much charge a capacitor can handle for a given voltage.

Question 20

A parallel plate capacitor creates a uniform electric field between the plates of the capacitor. What is Eds formula?

Answer 20

V = Ed

voltage between the plates of a capacitor equals the electric field times the distance between the plates.

Question 21

We can apply an outside voltage source to a capacitor to cause electron transfer between the two plates. This charges the capacitor. As we transfer more electrons against their natural gradient (i.e. against the electric field), it becomes increasingly difficult to move more electrons. What is the consequence?

Answer 21

By moving electrons “against nature,” we are increasing potential energy. Capacitors are a way of storing electric potential energy.

Question 22

What is the formula for the PE stored in a capacitor? Hint: Q = CV

Answer 22

PE = 1/2QV

Since Q = CV

PE = 1/2CV^2
or
PE = 1/2 x Q^2 / C

Question 23

What is capacitor discharge?

Answer 23

When you add a voltage source to transfer electrons to the positive plate, you are doing work against the electric field force (like lifting an object against gravity). When you allow the electrons to return to the positive plate down their gradient, say through a wire, this is called discharge.

Question 24

What is a dielectric? Dielectric constant?

Answer 24

Dielectrics are insulating materials that go between the plates of a capacitor to ensure they do not touch (i.e. discharge). Dielectrics always increase the capacitance

Thus, C = Ke A / d

K = dielectric constant of the material used

K = 1 for air or a vacuum

Question 25

Explain what the induced electric field is when a dielectric is used.

Answer 25

When you place a dielectric into a capacitor, the molecules of the insulating material become polarized. This polarization causes a small electric field (induced) that is opposite the E of the capacitor. This helps explain why a capacitors electric field is reduced when you use a dielectric.

Question 26

If you charge a capacitor, disconnect the battery, and then add a dielectric, what happens to C, V, PE, E and Q?

Answer 26

The dielectric increases capacitance so C increases.
If you disconnect the battery, then the charge on the plates cannot leave so Q is constant.

Q = CV. If C increases by k, then V must decrease by k
V = Ed. If V decreases by k, then E decreases by k
PE = 1/2QV. If V decreases by k and Q is constant, PE decreases by k

Question 27

If you charge a capacitor, leave it connected to the battery, and then add a dielectric, what happens to C, V, PE, E and Q?

Answer 27

The dielectric increases capacitance so C increases.
If you leave the battery connected, then voltage is constant.

Q = CV. If voltage is constant and C increases by a factor of k, Q must increase by k 
V = Ed. voltage is constant so E is constant 
PE = 1/2QV. V is constant and Q increases by k so PE must increase by k

Question 28

What is dielectric breakdown?

Answer 28

When the electric field becomes too strong between the two plates, the dielectric material can become ionized. This allows electrons on the negative plate to jump to the positive plate, discharging the capacitor very quickly. this is how lightning works.

Question 29

t or f, to add capacitors in a circuit, they follow the opposite rules to resistors.

Answer 29

true
series circuit - 1/C1 + 1/C2 + etc.
parallel circuit - C1 + C2 + etc.

Question 30

What is alternating current?

Answer 30

AC generators change their electric potential and can reverse their poles. In essence they change their voltage which allows current to flow in both directions through a wire (not at the same time)