1 © Unitec New Zealand APTE 5601+DE4401 Topic 2 DC C IRCUITS

Topic 1: Overview –Power –Circuit wiring Short circuit and open circuit –DC circuits Parallel circuits Series circuits Parallel-series combination circuits 2 © Unitec New Zealand

Power Power represents the work performed by an electric circuit (or, more accurately, rate at which work is done). Power is measured in watts (W). The electric power P (in watts, W) used in any part of a circuit is equal to the current I (in amperes, A) in that part multiplied by the voltage V (in volts, V) across that part of the circuit. 3 © Unitec New Zealand

Energy Energy is the capacity to do work. The unit of energy, called the joule (J), is used in scientific work to measure electric energy. In electrical circuits, power and time are factors that must be considered in determining the amount of energy used. This is usually done by multiplying kilowatts and multiplied by hours, the result is kilowatthours, abbreviated kWh. Energy measurements are used in calculating the cost of electric energy. A kilowatthour meter connected to a residential electrical system is used to monitor your daily power usage. 4 © Unitec New Zealand

Calculating electric power Determine power dissipated (released) in the lamp with internal resistance of 3 ohm connected to an 18V battery 5 © Unitec New Zealand

Solution: calculating power 6 © Unitec New Zealand

Double the voltage: what happens with P? 7 © Unitec New Zealand

Solution: 4 times more power 8 © Unitec New Zealand

Algebraic manipulation of power formula Using algebra again to manipulate the formulae, we can take our original power formula and modify it for applications where we don't know both voltage and current: 9 © Unitec New Zealand

Power rating for resistors Because resistors dissipate heat energy as the electric currents through them overcome the "friction" of their resistance, resistors are also rated in terms of how much heat energy they can dissipate without overheating and sustaining damage. Resistor resistance ratings cannot be determined from the physical size of the resistor(s) in question, although approximate power ratings can. The larger the resistor is, the more power it can safely dissipate without suffering damage. 10 © Unitec New Zealand

Exercise: Calculate power and energy Schaum’s Basic Electricity, page 42 to © Unitec New Zealand

Electric circuit Voltage from the battery is connected to the Load with resistance R. The current I flows through the circuit. 12 © Unitec New Zealand

Circuit wiring Connecting wires in a circuit are assumed to have zero resistance unless otherwise stated. Wires in a circuit can be shortened or lengthened without impacting the circuit's function. 13 © Unitec New Zealand Points directly connected together in a circuit by zero resistance (wire) are considered to be electrically common. Electrically common points will have zero voltage dropped between them. These rules apply to ideal conditions, where connecting wires are assumed to possess absolutely zero resistance. In real life this will probably not be the case, but wire resistances should be low enough so that the general principles stated here still hold.

Common points – ‘Ground’ 14 © Unitec New Zealand

Short circuit and open circuit 15 © Unitec New Zealand

Series and parallel circuits Circuits consisting of just one battery and one load resistance are very simple to analyze, but they are not often found in practical applications. Usually, we find circuits where more than two components are connected together. There are two basic ways in which to connect more than two circuit components: series and parallel. 16 © Unitec New Zealand

Series circuit In a series circuit, all components are connected end-to-end, forming a single path for current to flow. 17 © Unitec New Zealand

Total resistance of series circuit The total resistance of any series circuit is equal to the sum of the individual resistances 18 © Unitec New Zealand

Ohm’s law in series circuit In series circuits, the amount of current is the same through every component in the circuit 19 © Unitec New Zealand

Using table We can use Ohm's Law to determine the voltage drop across each resistor, one column at a time: 20 © Unitec New Zealand

Exercise 1: Series circuit Please go to Question 1 in your Worksheet 21 © Unitec New Zealand

Parallel circuit A parallel circuit is a circuit in which two or more components are connected across the same voltage source In parallel circuit, current is splitting in two paths, forming another “branch”. The point in which the current is splitting is called a node. 22 © Unitec New Zealand

Parallel circuit voltage is equal across all components in the circuit 23 © Unitec New Zealand

Total resistance in parallel circuit 24 © Unitec New Zealand

Calculating current : Ohm’s law 25 © Unitec New Zealand

(cont.) 26 © Unitec New Zealand

Exercise 2 Please go to Question 2 on your Worksheet 27 © Unitec New Zealand

Series - parallel combination circuit 28 © Unitec New Zealand In practice, we rarely find purely series or purely parallel circuits. Usually, the practical circuits are a mixture of these two. However, the rules still apply and are commonly used for the circuit analysis. Series Circuits: All components share the same (equal) current. Resistances add to equal total resistance. Parallel Circuits: All components share the same (equal) voltage. Resistances diminish to equal total resistance.

Example: Series-parallel combination 29 © Unitec New Zealand The goal of circuit analysis is to determine all voltage drops, currents and power dissipations in a circuit

Procedure overview To analyze a series-parallel combination circuit, follow these steps: –Reduce the original circuit to a single equivalent resistor, re- drawing the circuit in each step of reduction, as simple series and simple parallel parts are reduced to single, equivalent resistors. –Solve for total resistance. –Solve for total current (I=E/R). –Determine equivalent resistor voltage drops and branch currents one stage at a time, working backwards to the original circuit configuration again. 30 © Unitec New Zealand

Result 31 © Unitec New Zealand

Exercise 3 Please go to Question 3 on your Lab2 sheet 32 © Unitec New Zealand