Strand G Unit 3: Electrical Circuits. Introduction. Learning Objectives. Introduction. Key Facts and Principles.

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Diane Dawson
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1 Learning Objectives At the end of this unit you should be able to; Represent an electrical circuit using a circuit diagram. Correctly identify common components in a circuit diagram. Calculate current, potential difference and resistance in a series circuit for the whole circuit, and for individual components. Calculate current, potential difference and resistance in a parallel circuit for the whole circuit, and for individual components. Break down and simplify a combined series and parallel circuit, and determine current, potential difference. Describe the principles behind the parallel and series circuit rules. Apply Kirchoff s first Law and determine the current entering and leaving a circuit junction.. An electric current consists of charges that move from one region to another. If the charges move around a loop, this is an electrical circuit. As the charge moves around the circuit, electric potential energy is transferred from a source (such as a battery or cell) to a component in which that energy is either stored or used to do work. In the main there are two types of current in a circuit. A direct-current (dc), in which the direction of the current does not change with time, and alternating currents (ac), in which the current oscillates back and forth. Here we will concentrate on D.C circuits, which are the type obtained from a battery or cell. Electrical circuits can be quite complicated. They may use connecting wires or circuit board copper strips, filament bulbs or light emitting diodes, computer chips, or a large array of resistors connected in both series and parallel within the same circuit loop. In this unit we will learn how to simplify a complex circuit, applying different rules for series and parallel combinations allowing us to calculate voltages and currents of circuit elements. Key Facts and Principles. In a D.C circuit, the battery or cell is represented by two parallel lines, with one shorter than the other. The shorter line is always the negative (-) terminal whist the longer line is always the positive (+) terminal. The conventional current in a circuit is always the positive to the negative terminal of the cell. A series circuit is one in which all components are connected one after the other on the same loop. In a series circuit, The current flowing through each component is the same. In addition, the current measured anywhere in the circuit will be the same.

2 The total p.d across all the components is equal to the sum of the potential differences across each component. i.e. V0 = V1 + V2 + V3 For any complete loop, the sum of the emf s equals the sum of the p.d s round the loop. The total resistance is equal to the sum of the individual resistances, i.e. RT = R1 + R2 +R3 + Parallel circuits consist of two or more components connected to a cell in separate branches, similar to a ladder arrangement, providing two or more pathways that the current can follow. On a parallel circuit, the current can take an alternative route around the circuit if there is a break in one of the branches. Unlike a series circuit, parallel circuits contain current junctions; At any junction in a circuit, the sum of the currents entering the junction is equal to the sum of the currents leaving the junction. For parallel circuits; The potential difference across each component is the same. For two or more resistors in parallel, the total resistance RT is given by; 1 RR TT = 1 RR RR RR 3 + The total (combined) resistance is always less than the smallest of the individual resistances. For circuit calculations (which can get quite complicated) it is useful to put together a problem solving strategy. Review relevant concepts This encompasses the majority of concepts introduced in this strand, summarised as follows; II = QQ tt Current flows from the positive to negative terminal, electrons flow from the negative to positive terminal Potential difference (P.d) or voltage (V) is the work done (or energy transferred) per unit charge.

3 Work W is done when a charge Q flows through a component VV = WW QQ The emf (ε) is the energy per unit charge supplied to the circuit. The potential difference (p.d) or voltage is the energy used by, or the work done on components in the circuit. Electrical Power P is given by; PP = IIII Ohm s Law states; V = IR In a series circuit, the current flowing through each component is the same. At any junction in a circuit, the sum of the currents entering the junction is equal to the sum of the currents leaving the junction. For any complete loop, the sum of the emf s equals the sum of the p.d s round the loop For two or more components in series, V0 = V1 + V2 + V3 For components connected in parallel, the potential difference across each component is the same. For resistors in series, RT = R1 + R2 +R3 + For resistors in parallel, 1 RR TT = 1 RR RR RR 3 + Set Up the Problem 1. Make a drawing of the circuit. This will help to split the circuit up into easier chunks in order to solve. 2. Identify all components. 3. Identify sources of emf and of p.d so that concepts such as the sum of the emf equals the sum of the p.d on a closed loop, or the p.d of resistors in parallel equal the emf of the source may be used. 4. Identify the required quantity

4 Solve the Problem 1. Simplify where possible. 2. Combine parallel resistors into a combined resistance 3. Combine series resistors in complex problems 4. Calculate total resistance of the circuit to find current drawn 5. Employ the junction rule to find the current in each branch Remember that a diode only passes current in one direction. Also, for more than one cell in series, the individual emf s may be added. Evaluate There are always different ways to solve a problem. For instance, junction rules could be used to solve for currents in a parallel branch, but also the individual resistance could be used along with the source voltage. Check your answers by solving both ways. Also remember the combined resistance of a set of parallel resistors can never be greater than the smallest resistance value in the combination. And don t forget to take the inverse when calculating the resistance of parallel resistors!

5 Glossary Alternating Current (A.C) A current that continuously reverses direction with time Cell (electrochemical) A device capable of changing chemical energy into electrical energy, providing the electromotive force to a circuit. Two or more cells connected in series constitute a battery. Conventional Current Charge flow under the influence of an electric field, in the direction of positive charge flow. Diode A device that allows charge flow in one direction only. Emf The electromotive force (emf) is the electric potential per unit charge supplied by a cell or battery. Parallel (circuit) A closed circuit in which the current divides into two or more paths via a current junction (forming multiple current loops) before recombining to complete the circuit. P.d The energy per unit charge used by, or the difference in electrical potential energy between the contacts of a component in a circuit. Series (circuit) An electrical circuit in which the current follows a single path, passing through components sequentially without branching.

Unit 3. Electrical Circuits

Strand G. Electricity Unit 3. Electrical Circuits Contents Page Representing Direct Current Circuits 2 Rules for Series Circuits 5 Rules for Parallel Circuits 9 Circuit Calculations 14 G.3.1. Representing