Circuits

The SI units for electrical PE are…

joules

What are the accepted symbols for electric potential energy?

U

PE

How would you increase the electrical potential energy of a pair of charged particles of the SAME sign?

decrease their separation

How would you decrease the electrical potential energy of a pair of OPPOSITELY charged particles?

decrease their separation

How would you decrease the electrical potential energy of a pair of charged particles of the SAME sign?

increase their separation

How would you increase the electrical potential energy of a pair of OPPOSITELY charged particles?

increase their separation

Equation for computing the electrical potential energy stored in a pair of charged particles

K\frac{q1q2}{r}

Electric potential energy is a (scalar/vector) quantity

scalar

It may increase or decrease, but it has no compass direction.

When charged particles are released and can move freely, their electric potential energy will be converted to…

kinetic energy

Units for electric potential

volts

Is electric potential a scalar or vector

scalar

volts in terms of joules/coulombs

1 V = 1 J/C

Electric fields point in the direction that ___ charges freely move when released.

positive

Electric fields point towards locations of ___ potential.

lower

Which way do positively charged particles freely move towards?

direction of lower potential

Which way do negatively charged particles freely move towards?

direction of higher potential

 

Locations of higher electric potential are _____ positively charged bodies than locations of lower potential

closer to

What are equipotential surfaces?

locations of the same potential in an electric field

Equipotential surfaces are ___ to electric field vectors

perpendicular

If a location in an electric field has a potential of 10 V, it means that 1 coulomb of charge would ________ at this location

possess 10 J of potential energy

Is potential constant in an uniform electric field?

no

potential changes as you move from one position to another. an electric field is a potential gradient.

If a charged particle moves freely in an electric field, its PE…

decreases

How does the capacitance of a capacitor increase?

• increase area (make plates bigger)

• decrease r (decrease separation of plates)

• use more polar dielectric

The places of capacitors are (insulators/conductors)

conductors

Dielectric is a (insulator/conductor)

insulator

What do capacitors do?

• provide a quick burst of energy in automated external defibrillators

• provide a quick burst of current in a computer keyboard

• maintain a uniform electric field in air purifiers

How would you increased the energy stored in a capacitor?

charge it with a higher voltage battery

Units for capacitance

farads (F)

Equation for finding sum of capacitors in series

\frac{1}{Ceq} = \frac{1}{C1} + \frac{1}{C2} + … \frac{1}{Cn}

Equation for finding sum of capacitors in parallel

Ceq = C1 + C2 + … Cn

Characteristics of equipotential surfaces/lines/contours

• perpendicular to electric field lines

• areas where electric potential is the same, regardless of object’s charge

• concentric spheres around a single source charge

• equipotential contours can never meet or cross

• contours are closer = more electric potential energy

test charges seek (higher/lower) energy states

lower

(think of a ball rolling down an incline)

The electric potential energy of interaction of two charged objects is defined to be zero when the distance between them is ____

infinitely far away

If two objects have the same sign charges, their electric potential energy is (positive/negative)

positive

If two objects have opposite charges, their electric potential energy is (positive/negative)

negative

If two oppositely charged objects move closer together, their electric potential bar will (increase/decrease) in size

increase

if the Ue between two equal charges quadruples, what happens to the distance between the particles?

distance decreases by a factor of 4 → 1/4

When is the equation ∆Ue = -qEdcosθ used?

when a charge, q, moves freely in an electric field

Electric potential definition

the electric potential at a point is defined as the amount of electric potential energy a positive test charge would have if placed there, the energy per unit charge

Equation for electric potential, V

V = Uq/q

How to calculate electric potential of multiple point charges?

add the V values together

Compare electric potential and electric field

electric field is force per charge

electric potential is energy per charge

Potential difference (∆V)

voltage, the difference between the electric potential a the final location minus the electric potential at the initial location

∆V = Vf-Vi

What does a negative ∆V signify?

decrease in V (high → low)

What does a positive ∆V signify?

increase in V (low → high)

Describe the force on a charged particle placed anywhere in an uniform field

the force is constant everywhere

What is the equation ∆V = -Edcosθ used for?

the charge of 1 Coulomb of charge experiences when it is displaced a distance “d“ in a uniform electric field. θ is the angle between the E-field and the displacement of charge.

The minus sign indicates E pointing in the direction of decreasing potential

at 0°, E and d are in the same direction

Will the electric field inside the dielectric be zero?

No.

(The electric charges do not flow through the dielectric as they do in a conductor (dielectrics are insulators). The electric field can be reduced, but cannot be minimized to zero. In addition, the dielectric constant k cannot be zero since it is a measure of a material’s ability to store electric energy in an electric field.)

How is k, the dielectric constant, related to E?

as k increases, E (net E-field) weakens

What is capacitance?

how much charge accumulates on 1 plate per volt applied across the plates

C = Q/V

___ plates are the most common type of capacitor

parallel

what is ε

8.85 × 10^-12 F/m

permittivity of free space

for parallel capacitors, what occurs when the dielectric is inserted into the capacitor?

capacitance increases

What happens to the charge on a parallel plate capacitor is the potential difference doubles?

capacitance stays the same, Q doubles

Do uncharged parallel plates still have a capacitance?

yes

Why is Ue for a capacitor referred to as stored energy?

energy is stored in the electric field between the capacitor’s plates. as the capacitor is being charged, the electric field builds up.

Which quantities (Q, C, or Ue) change when using a higher voltage power supply to charge a capacitor?

Q, Ue

A parallel plate capacitor is charged and then disconnected from a battery. how does the stored energy change when the plate separation is doubled?

Q and V stay the same. Energy doubles

why is it dangerous to touch the terminals of a high-voltage capacitance even after the potential difference has been removed?

because capacitors still hold charge

What does discharging do?

make the capacitor safe to handle after potential difference has been removed.

Why do two metal plates near each other not become charged until connected to a source of potential difference?

Both plates start neutral. If there is no potential difference, there is no electric force to set charges into uniform motion. By providing voltage, there is a potential difference, allowing for motion.

What does the area under the curve of a current vs. time graph represent?

total charge placed on capacitor

How are capacitors charged?

electrons flow from negative terminal of battery to empty capacitor plate → repel electrons from other plate → repelled electrons flow back to battery

Describe a graph that depicts charge vs. time as a capacitor is being charged

Starts at zero, increases, slows down until it reaches potential difference (looks like a log. graph)

Describe a graph that depicts potential (v) vs. time as a capacitor is being charged

Starts at zero, increases, slows down until it reaches potential difference (looks like a log. function)

Describe a graph that depicts current vs. time as a capacitor is being charged

really high, decreases as potential get closer to battery’s potential (looks like exponential decay function)

Describe a graph that depicts current vs. time as a capacitor is being discharged

really high → decreases to zero point when it is fully discharged so there is no more current (looks like exponential decay function)

Describe a graph that depicts charge vs. time as a capacitor is being discharged

rate of decrease proportional to current (starts high → decreases)

Describe a graph that depicts potential (v) vs. time as a capacitor is being discharged

rate of decrease proportional to current (starts high → decreases)

Would capacitors connected in parallel or in series have a greater time constant (time it takes to discharge a capacitor)?

capacitors in parallel

(t = RC, R = resistance. you want a higher C)

Characteristics of Q and V for capacitors in series

Q is equal

V is split

Characteristics of Q and V for capacitors in parallel

V’s are equal

Q is split

What could you change in a circuit to increase the charge stored in a capacitor?

increase potential difference

remove all the other capacitors

What happens to the resistor over time when the switch is closed?

the current starts high → slowly becomes lover → zero

What happens to the potential difference across a resistor when the switch is open and after the switch is closed?

voltage starts high → plummets quickly → zero

What happens to the potential difference across a capacitor when the switch is open and after the switch is closed?

voltage starts low → rises gradually

What does a capacitor act as when fully charged?

an open switch

What is steady state?

everything in equilibrium, capacitor is fully charged

What factors affect the amount of time required for the circuit to reach steady state?

capacitance, resistance

increasing capacitance → amount of charge increases → takes longer to reach steady state

What happens qualitatively if the switch was opened after the switch had reached steady state?

nothing happens because it is in equilibrium

What quantities at steady state would be different if ∆V across the battery was increased?

charge, current, time needed to reach steady state, ∆V

What quantities at steady state would be different if the resistance of the resistor was increased?

current, time (increases)

(∆V does not change, therefore Q does not change)

Current takes the path of ___ resistance

least

(will typically go through capacitors first → capacitors are fully charged → go through resistors)

How to calculate current

I = ∆V/R