Current and Resistance

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:

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

(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:

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:

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

(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:

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.