Download Current and Resistance Electric Circuit – Current – Equation: Units

Current and Resistance
Electric Circuit –
Current –
Equation:
Units:
Conventional current –
**usually, _______________ do most of the moving, so the direction of positive current flow is opposite
the direction the ________________ are actually flowing
Conductivity and Resistivity
Electrical charges move more easily through ______________ and less freely through _________________
Conductivity (Define):
Depends on:
1.
2.
Resistivity (Define):
Equation:
Units:
(for this unit, we mostly speak about resistivity)
*Is dependent on ______________, often resistivity is given at a certain _____________ to make sure that it
doesn’t change because of ________________.
For a metal, as temperature increases, resistivity increases, example:
Resistance:
*is a function of both the __________ and the _______________ of the device
Equation:
Units:
Ex1. The five resistors shown below have the lengths and cross–sectional areas indicated and are
made of material with the same resistivity. Which has the greatest resistance?
Resistors:
A resistor is a circuit element – the resistance of a resistor tells you how well it impedes the flow of
current. The ____________________ of a resistor tells you how well it impedes the current flow, and it
depends on the resistors ____________________ and the _________________________ of the material
*Color bands on a ceramic resistor tell you what the resistance of that resistor is (you look it up on a
chart)
A light bulb is also a resistor, a resistor is drawn like this:
A light bulb will often be seen on the AP test, when it is, you can just treat it as a resistor.
Configuration of a Resistor:
- When put into a circuit, a resistor can be situated either in series or in parallel
- To make it easier to analyze, a equivalent resistance can be calculated that sums up all of the
resistance from the resistors with a single equivalent resistance
Resistors in Series:
One current path, this means that the ENTIRE series will have the same current (important because
this will help you with figuring out more complex circuits), but will share the voltage, so to
determine equivalent resistance just:
Ex:
Resistors in Parallel:
Resistors in parallel have the same voltage flowing through them, but the current is shared between
them. Multiple Current paths, so the way to sum up equivalent resistance is:
**Equivalent resistance in parallel is always less than the smallest resistor…
Ex:
If you only have two resistors in parallel, you can use a shortcut equation to determine the
equivalent resistance (very useful as we get into more complex problems):
Equation:
Ex2. Which two arrangements of resistors shown above have the same resistance between the
terminals?
(A) I and II (B) I and IV (C) II and III (D) II and IV (E) III and IV
Ex3. The total equivalent resistance between points X and Y in the circuit shown above is
(A) 3 Ω (B) 4 Ω (C) 5 Ω (D) 6 Ω (E) 7 Ω
Ex4. Two resistors of the same length, both made of the same material, are connected in a series to
a battery as shown above. Resistor II has a greater cross. sectional area than resistor I. Which of the
following quantities has the same value for each resistor?
(A) Potential difference between the two ends
(B) Electric field strength within the resistor
(C) Resistance
(D) Current per unit area
(E) Current
Ohm’s Law and Power:
Equation:
*This law is not obeyed by all materials, however, it is very useful for:
1.
2.
To test to see if a material follows Ohms law, plot voltage vs. current:
Ohmic materials show a ___________________ relationship.
Electrical Power
Current flowing through a circuit causes energy to transfer into other types of energy. The
____________ at which electrical energy transforms into other types of energy is ____________ to the
electrical power dissipated
Light Bulb =
Television =
Calculating Power – rate at which energy is provided by battery or consumed by the resistor
Equation:
Units:
*On an electric bill, energy is shown in kilowatt-hours (kW*hr), which is a unit of ________________
Ex5. An immersion heater of resistance R converts electrical energy into thermal energy that is
transferred to the liquid in which the heater is immersed. If the current in the heater is I, the
thermal energy transferred to the liquid in time t is
(A) IRt (B) I2Rt (C) IR2t (D) IRt2 (E) IR/t
Ex6. When lighted, a 100–watt light bulb operating on a 110–volt household circuit has a resistance
closest to
(A) 10–2 Ω (B) 10–1 Ω (C) 1 Ω (D) 10 Ω (E) 100 Ω
Ex7. In a 30-minute interval, one kilowatt-hour of electrical energy is dissipated in a resistance of
20 ohms by a current of
(A) 10 amp. (B) 20 amp. (C) 14.1 amp. (D) 36 amp. (E) 18 amp.
Electrical Circuits (define):
Circuits can be made of many different materials (you can be part of one if you aren’t careful),
however, most consist of:
Conventional current flows from _________________ potential to ______________ potential
**remember, electrons are the opposite, they flow from ___________ potential to ___________ potential
We can draw a 2-D circuit schematic to represent a 3-D electrical circuit, in general, symbols
represent circuit elements and lines represent wires. Some of the symbols that we will be using to
draw our circuit schematics are:
**A source of potential difference in required for current to flow
**Current only flows in ____________________ _________________________
A _______________________ measures the potential difference between two points in a circuit
It is always connected in _______________, and if removed from the circuit, it _______________ break the
circuit
It has a very ______________ resistance. Why?
Draw one:
An _______________________ measures current flowing through an element of the circuit
It is always connected in _______________, and if removed from the circuit, it _______________ break the
circuit
It has a very ______________ resistance. Why?
Draw one:
Series circuits only have a single current path. So, if you remove any circuit element (or if it
breaks), what will happen?
___________________ Laws – very important tools for analyzing circuits
KCL = ____________________ ______________________ __________________:
-
Also called the Junction Rule – the current going into a junction must equal the current
going out
KVL = ____________________ ______________________ __________________:
-
is a restatement of Conservation of Energy –
Also called the Loop Rule
Basic Series Circuit Analysis:
V
I
R
P
Total:
If you know any two numbers in a row, you can find the others in that row…
(please write out everything fully on your own paper, as we progress to more complex circuits,
these initial ones will come in handy to understand them completely)
_____________ is always the same in a series circuit.
Parallel Circuits – have multiple current paths. So, if you remove one circuit element (or it breaks),
what will happen to the rest of the circuit?
Basic Parallel Circuit Analysis:
V
I
R
P
Total:
_____________ is always the same in a parallel circuit.
For a combination of Series-Parallel Circuits, you can complete a few simple steps to make it easier
to work through:
1.
2.
3.
Ex8. In the circuit shown above, what is the value of the potential difference between points X and Y
if the 6–volt battery has no internal resistance?
(A) 1 V (B) 2 V (C) 3 V (D) 4 V (E) 6V
Ex9. A lamp, a voltmeter V, an ammeter A, and a battery with zero internal resistance are connected
as shown above. Connecting another lamp in parallel with the first lamp as shown by the dashed
lines would
(A) increase the ammeter reading
(B) decrease the ammeter reading
(C) increase the voltmeter reading
(D) decrease the voltmeter reading
(E) produce no change in either meter reading
Ex10. The total equivalent resistance between points X and Y in the circuit shown above is
(A) 3 Ω (B) 4 Ω (C) 5 Ω (D) 6 Ω (E) 7 Ω
Ex11. What is the current I1?
(A) 0.8 mA (B) 1.0 mA (C) 2.0 mA (D) 3.0 mA (E) 6.0 mA
Ex12. How do the currents I1, I2, and 13 compare?
(A) I1 > I2 > I3 (B) I1 > I3 > I2 (C) I2 > I1 > I3 (D) I3 > I1 > I2 (E) I3 > I2 > I1
Ex13. In the circuit shown above, the current in each battery is 0.04 ampere. What is the potential
difference between the points x and y?
(A) 8 V (B) 2 V (C) 6 V (D) 0 V (E) 4 V
Ex14. In the circuit shown above, what is the resistance R?
(A) 3 Ω (B) 4 Ω (C) 6 Ω (D) 12 Ω (E) 18 Ω
In the circuit above, the emf's and the resistances have the values shown. The current I in the circuit
is 2 amperes.
Ex15. The resistance R is
(A) 1 Ω (B) 2Ω (C) 3 Ω (D) 4 Ω (E) 6 Ω
Ex16. The potential difference between points X and Y is
(A) 1.2 V (B) 6.0 V (C) 8.4 V (D) 10.8 V (E) 12.2 V
Ex17. How much energy is dissipated by the 1.5–ohm resistor in 60 seconds?
(A) 6 J (B) 180 J (C) 360 J (D) 720 J (E) 1,440 J
Ex18. What is the current through the 6.0 Ω resistor shown in the accompanying circuit diagram?
Assume all batteries have negligible resistance.
(A) 0 (B) 0.40 A (C) 0.50 A (D) 1.3 A (E) 1.5 A
Ex19. The circuit above contains a battery with negligible internal resistance, a closed switch S, and
three resistors, each with a resistance of R or 2R.
a. i. Rank the currents in the three resistors from greatest to least, with number 1 being greatest. If
two resistors have the same current, give them the same ranking.
_______IA _______IB _______Ic
ii. Justify your answers.
b. i. Rank the voltages across the three resistors from greatest to least, with number 1 being
greatest. If two resistors have the same voltage across them, give them the same ranking.
_______VA _______VB _______Vc
ii. Justify your answers.
For parts c. through e., use E = 12 V and R = 200 Ω.
c. Calculate the equivalent resistance of the circuit.
d. Calculate the current in resistor RC
e. The switch S is opened, resistor RB is removed and replaced by a capacitor of capacitance 2.0 ×
10–6 F, and the switch S is again closed. Calculate the charge on the capacitor after all the currents
have reached their final steady-state values.
Internal Resistance – previously, we have been using ideal voltage sources, batteries, etc – but in
reality, sources have some amount of internal resistance (even if very small)
 In reality, sources all have some amount of ______________ ____________________ (however small)
 ________________________ ______________________ of the voltage source is actually reduced slightly
by the potential drop of current flowing through the internal resistance. Equation for this:
RC Circuits
Capacitors in Parallel (combine like ____________________ in ___________________) – store charge on their
plates (can be replaced with an equivalent capacitor)
Capacitors in Series (combine like __________________ in ______________________) charge between the
positive plate of one capacitor and the negative plate of the next capacitor in the series must be the
same – can be replaced with an equivalent capacitor
RC Circuits are made up of:
1.
2.
3.
Steady state perspective:
1. What happens when they are first turned on?
2. What happens after a long time has elapsed?
**Key to understanding RC Circuits
- Uncharged capacitors act like _________________
- Charged capacitors act like ______________________
Assume the capacitor C is initially uncharged. The following graphs may represent different
quantities related to the circuit as functions of time t after the switch S is closed
Ex20. Which graph best represents the voltage versus time across the resistor R?
(A)A (B)B (C)C (D)D (E) E
Ex21. Which graph best represents the current versus time in the circuit?
(A)A (B)B (C)C (D)D (E) E
Ex22. Which graph best represents the voltage across the capacitor versus time?
(A)A (B)B (C)C (D)D (E) E
Below is a system of six 2–microfarad capacitors.
Ex23. The equivalent capacitance of the system of capacitors is
(A) 2/3μF (B) 4/3 μF (C) 3 μF (D) 6 μF (E) 12 μF
Ex24. What potential difference must be applied between points X and Y so that the charge on each
plate of each capacitor will have magnitude 6 microcoulombs?
(A) 1.5 V (B) 3V (C) 6 V (D) 9 V (E) 18 V
In the circuit shown above, the battery supplies a constant voltage V when the switch S is closed.
The value of the capacitance is C, and the value of the resistances are R1 and R2.
Ex25. Immediately after the switch is closed, the current supplied by the battery is
(A) V/(R1 + R2) (B) V/R1 (C) V/R2 (D) V(R1 + R2)/R1R2 (E) zero
Ex26. A long time after the switch has been closed, the current supplied by the battery is
(A) V/(R1 + R2) (B) V/R1 (C) V/R2 (D) V(R1 + R2)/R1R2 (E) zero
Ex27. In the circuit shown above, A and B are terminals to which different circuit components can
be connected.
a. Calculate the potential difference across R2
i. A 50 Ω resistor connects A and B. immediately after the switch S is closed in each of the
following cases.
ii. An initially uncharged 0.80 μF capacitor connects A and B.