Chapters 22 and 23 notes and sample problems.
Last modified April 22, 1998.
Electric circuits transfer energy. Electrical energy is converted into light, heat, sound, mechanical work, etc. The byproduct of any circuit is always heat.
DC current (direct current) - consists of a steady flow of current in one direction
AC current (alternating current) - direction of current flow changes many times a second. In the US, the frequency of change is 60 Hz. Therefore, the current changes direction 120 times per second.
emf (electromotive force) - source of energy moving electrons through the circuit
electric current (symbol is I; SI unit is the ampere, or A) - flow of charge current = charge/sec or 1 A = 1 C/ sec
electric power (symbol is P; SI unit is watt) - the rate of doing electrical work P = VI or P = I2R 1 W = 1 J/sec = 1 V A
electrical work (symbol is W; SI unit is Joule): W = Pt or W = V I t
Ohm's Law resistance (symbol is R; SI unit is ohm or () - opposition to current flow 1 ( = 1 V/ 1 A
Ohm's law - for a given resistance, the potential difference is proportional to the current flow V = I R
Resistance of a solid conductor depends upon: 1. nature of the material 2. length of the conductor 3. cross-sectional area of the conductor 4. temperature
galvanometer - measures small currents
ammeter - measures current
ammeters and galvanometers are connected in a circuit, positive to positive and negative to negative; they have very low resistance so that the current flow through them is a maximum; they are connected in series
voltmeter - measures potential difference between two points in a circuit
voltmeters are connected in a circuit, positive to negative and negative to positive. They have very high resistance so that the current flow through them is a minimum; they are connected in parallel
1. A 12 V battery is connected in a circuit. An ammeter reads 2 A. What resistance is connected in the circuit? What power is dissipated in the circuit? What electrical power is used after 4 sec?
2. Repeat number one using a 120 V battery, an ammeter reading 1.5 A, and a time of 3 min.
3. An 8 ohm resistor, a switch, and a 12 V battery are connected in a circuit. Draw the circuit diagram. Calculate the current.
4. A 60 W bulb is connected to 120 V. What is its resistance?
5. A 30 W bulb is connected across 120 V. What is its resistance? What electrical work is used in 10 sec?
Series circuit - resistors are connected so that there is only one path for the current to flow through the resistors; the current is the same at all points - current is constant in series
effective resistance (equivalent resistance)- the resistance of a single resistor that could replace all the resistors in a series circuit
Kirchoff's second law - in any closed circuit loop, the potential energy drops of the individual electrical devices equals the total energy of the circuit; this is a statement of the law of conservation of energy
As resistors are added in series, total resistance increases and total current decreases.
Steps in simplifying series circuits: 1. find the effective resistance of the circuit 2. find the total current using Ohm's law 3. apply Ohm's law to each individual resistor to determine the individual resistor's voltage drop
1. A circuit consists of a 5 W and a 10 W resistor connected in series across a 45 V battery. A voltmeter is connected across each resistor. An ammeter measures total current. A switch is also included. Calculate the total current and the voltage drops across each resistor. Draw the circuit.
2. A 5 W, a 10 W, and a 15 W resistor are connected in series. Each has a voltmeter. A switch and an ammeter are included as well as a 30 V battery. What does the ammeter read? What is the voltmeter reading of the 10 W resistor? Draw the circuit.
3. A 2 W, a 6 W, a 4 W, and an unknown resistor are connected in series with a 6 V battery. An ammeter reads 0.25 A. What is the value of the unknown resistor? What does a voltmeter across the 4 resistor read? What power is dissipated in the 6 W resistor? What electrical energy is used by the 6 resistor in 20 sec?
4. A 2 W, a 1 W, a 4 W, and an unknown resistor are connected in series using a 12 V battery. An ammeter reads 1.50 A. What is the magnitude of the unknown resistor? What power is dissipated in the 4 W resistor? What electrical energy is used by the 4 W resistor in 10 sec?
5. An unknown resistor and a 60 W light bulb are connected in series with a 120 V battery. An ammeter reads 1.50 A. What is the magnitude of the unknown resistor?
Parallel circuits - resistors in parallel have the same voltage drop across them. The sum of the currents in each parallel branch equals the total current entering the parallel branch of resistors. Voltage is constant in parallel.
Kirchoff's first law - the sum of the currents entering a point is equal to that of the currents leaving the point.
In a parallel circuit, all the resistors in parallel can be replaced with one equivalent resistance that carries the same current and has the same voltage drop across it.
As resistors are added in parallel, total resistance decreases and total current increases.
Power companies maintain a house voltage of 120 V. House appliances are connected in parallel. The more appliances on a circuit, the lower the total resistance, the greater the current. Fuses protect against circuit overloading.
Steps in simplifying parallel circuits: 1. find the equivalent resistance 2. use Ohm's law to find total current 3. apply Ohm's law to each resistor to find the current in that branch
1. A 12 W, a 20 W, and a 24 W resistor are connected in parallel across 120 V. Each resistor has its own voltmeter and ammeter. Also, an ammeter reads total current. A switch is located in the main circuit. Draw the circuit. Calculate total resistance. Determine the total current. Calculate each voltmeter and ammeter reading.
2. Four 18 W lamps are connected in parallel across 6 V. What is the current in each? What is the resistance of each? What is the effective resistance of the circuit?
3. A 60 W, a 20 W, and a 10 W resistor are connected on a house line. Will a 25 A fuse blow?
Complex circuits are a combination of resistors in parallel and in series.
Steps in simplifying complex circuits: 1. determine the equivalent resistance of each set of resistors in parallel 2. determine the total resistance of the circuit 3. determine total current 4. calculate voltage drops across all series resistors 5. calculate currents in each parallel branch
1. A 36 W resistor is connected in series with parallel resitors of 48 W and 16 W. A 48 V battery is used. Each resistor has its own voltmeter. Each parallel branch has its own ammeter. An ammeter measures total current. Find each meter reading.
2. A 12 W and a 10 W resistor are connected in parallel. Each has its own voltmeter and ammeter. A 6 W resistor is connected in series with the two parallel resistors. It has its own voltmeter. An ammeter reads total current. A 9 V battery is used. Find each meter reading.