1. CIRCUIT ANALYSIS I

2. TOPIC
1. Ohm’s Law
2. Power
3. Energy

3. Review of V, I, and R Voltage is
the amount of energy per charge available to
move electrons from one point to another in a circuit.
the rate of charge flow and is measured in
amperes.
Current is
the opposition to current and is measured
in ohms.
Resistance is

4. 1. Ohm’s Law
The most important fundamental law in electronics is Ohm’s law, which relates voltage, current, and resistance.
Georg Simon Ohm ( ) studied the relationship between voltage, current, and resistance and formulated the equation that bears his name.
Question:
What is the current in from a 12 V source if the resistance is 10 W?
1.2 A

5. Formula for voltage Question: Ohm’s law
If you need to solve for voltage, Ohm’s law is:
Question:
What is the voltage across a 680 W resistor if the current is 26.5 mA?
18 V

6. Formula for resistance
Ohm’s law
If you need to solve for resistance, Ohm’s law is:
What is the (hot) resistance of the bulb?
Question:
115 V
132 W

7. The linear relationship of Current and Voltage
A student takes data for a resistor and fits the straight line shown to the data. What is the resistance and the conductance of the resistor?
Graph of Current versus Voltage
The slope represents the conductance.
The reciprocal of the conductance is the resistance:

8. The linear relationship of Current and Voltage
Graph of Current versus Voltage
Notice that the plot of current versus voltage for a fixed resistor is a line with a positive slope. What is the resistance indicated by the graph?
2.7 kW
What is its conductance?
0.37 mS

9. Graph of Current versus Voltage
R constant
Increase V, I increase
Decrease V, I decrease

10. Graph of Current versus Resistance
If resistance is varied for a constant voltage, the current verses resistance curve plots a hyperbola.
Question:
What is the curve for a 3 V source?

11. Graph of Current versus Resistance
V constant
Increase R, I decrease
Decrease R, I increase

12. Application of Ohm’s law
26.8 mA
The resistor is green-blue brown-gold. What should the ammeter read?

13. 2. Energy
Energy, W, is the ability to do work and is measured in joules. One joule is the work done when a force of one newton is applied through a distance of one meter.
1 m
The symbol for energy, W, represents work, but should not be confused with the unit for power, the watt, W.

14. Power
Power is the rate energy is “used” (actually converted to heat or another form). Power is measured in watts (or kilowatts). Notice that rate always involves time.
One watt = one joule/second

15. Example 2.1
An amount of energy equal to 100 J is used in 5 s. What is the power in watts?

16. The Kilowatthour (kWh) unit of Energy

17. The Kilowatthour (kWh) unit of Energy
The kilowatt-hour (kWh) is a much larger unit of energy than the joule. There are 3.6 x 106 J in a kWh. The kWh is convenient for electrical appliances.
Question:
What is the energy used in operating a 1200 W heater for 20 minutes?
1200 W = 1.2 kW
20 min = 1/3 h
W = P x t
= 1.2 kW X 1/3 h =0.4 kWh

18. Example 2.2
Determine the number of kilowatthours for each of the following energy consumptions:
1400 W for 1 hour
2500 W for 2 hours
100,000 W for 5 hours

19. Example 2.3
If a power company charges RM 0.10 for each kWh of energy delivered to a customer, find the total cost of operating a 500 W television set for 2 hour, six 75 W light bulbs for 4 hour, a 1500 W clothes drier for 30 min and 2kW electric heater for 45 minutes.

20. Example 2.4
If electrical energy costs RM 0.12/kWh, for how long could a 900 W oven be operated without costing more than 36 cents.

21. Power in electric circuit
Three equations for power in circuits that are collectively known as Watt’s law are:

22. Power Example 2.5 Calculate the power in each of three circuits below:
10 V V
5 V
47 Ω
10 Ω
(a) (b) (c)

23. Power
Example 2.6
A 100 W light bulb operates on 120 V. How much current does it require?

24. Power Resistor Power Rating
A resistor gives off heat when there is current through it.
There is a limit to the amount of the heat that a resistor can give off, which is specified by its power rating.
The power rating is the maximum amount of power that a resistor can dissipate without being damaged by excessive heat buildup.
The power rating is not related to ohmic value (resistance) but rather determined by the physical size and shape of the resistor.
The larger the surface area of resistor, the more power it can dissipate

25. How to select the proper power rating for an application
When a resistor is used in circuit, its power rating must be greater than the maximum that it will have to handle.
For example, if a carbon-composition resistor is to be dissipate 0.75 W in a circuit application, its rating should be at least next higher standard value which is 1 W.

26. Power
Example 2.7
Choose the power rating for each of the resistor in figure below:
10 mA
10 V V
62 Ω
1000 Ω

27. Resistor failures
Resistor failures are unusual except when they have been subjected to excessive heat. Look for discoloration (sometimes the color bands appear burned). Test with an ohmmeter by disconnecting one end from the circuit to isolate it and verify the resistance. Correct the cause of the heating problem (larger resistor?, wrong value?).
Normal Overheated

28. Power
Example 2.8
Determine whether the resistor in each circuit below has possibly been damaged by overheating.
¼ W
62 Ω
½ W
100 Ω
9 V V

29. Energy loss and voltage drop in a resistance
Electrons are flowing out of the negative terminal of the battery.
They have acquired energy from the battery and are at their highest energy level at the –ve side of the circuit.
As the electron move through the resistor, they lose energy.

30. Energy loss and voltage drop in a resistance
The electrons emerging from the upper end of the resistor are at a lower energy level than those entering the lower end.
The drop in energy level through the resistor create a potential differences or voltage drop, across the resistor.

31. Selected Key Terms Linear Ohm’s law Troubleshooting
Characterized by a straight-line relationship.
A law stating that current is directly proportional to voltage and inversely proportional to current.
A systematic process of isolating, identifying, and correcting a fault in a circuit or system.

32. George Simon Ohm