What is an Electric Current?

Electric Circuits NTODUCTON: Electrical circuits are part of everyday human life. e.g. Electric toasters, electric kettle, electric stoves All electrical devices need electric current to operate. n this section we study charges in motion called electric current. Electric Current esistance and Ohm s Law and resistivity Energy and Power in Electric Circuits esistors in Series and Parallel Equivalent resistive circuits

What is an Electric Current? Electric current is the rate at which electric charges move through a wire or a conductor (flow of electric charges). Structure of the atom: -Protons and Neutrons fixed in the Nucleus -Electrons move in different energy levels. alence electrons are free to move PATCLE CHAGE MASS Electron.6 0-9 C 9. 0-3 kg Proton.6 0-9 C.67 0-27 kg Neutron No charge.67 0-27 kg 2

Electronic Current Conventional Current f a charge, dq, passes through a given cross-section of a conductor in a time, dt, then a current,, is said to have passed, where: q S. UNTS: dq dt t 0 dt Charge in Coulombs (C) Time in Seconds (s) Current in Amperes (A) Time interval dt Direction of positive flow 3

ELECTOMOTE FOCE (EMF) Any device which causes Charge separation to occur is said to be a source of electromotive force or EMF. i.e. A battery with EMF,, provides energy to the charges to make them move through a wire. S. unit: OLT () A battery that is disconnected from any circuit has an electric potential difference between its terminals that is called the electromotive force or EMF: emember despite its name, the EMF is an electric potential or voltage, not a force. Electric circuit: A closed path through which charge can flow, returning to its starting point, is called an electric circuit. i.e. A closed path is required for current to flow. 4

A battery uses chemical reactions to produce a potential difference between its terminals. t causes current to flow through the flashlight bulb similar to the way the person lifting the water causes the water to flow through the paddle wheel. When the switch is closed, it provides a closed path for electric charges to flow. i.e. the battery sends out positive charges from the positive terminal and accepts them at the negative terminal. 5

Electric Current The direction of current flow from the positive terminal to the negative one was decided before it was realized that electrons are negatively charged. Therefore, current flows around a circuit in the direction a positive charge would move; electrons move the other way. However, this does not matter in most circuits. Conventional current always tries to flow from the positive terminal to the negative terminal of the battery. The symbol of the battery: Conventional current Electronic current 6

We use circuit symbols to make understanding of circuits easier. Shown are some common circuit symbols: Ammeter 7

Consider a circuit of battery connected to a light bulb as shown: A Bulb f we measure the current with an ammeter we find that it has same finite value everywhere in the circuit. e.g. A or 0.0 A f another bulb is added to the circuit, current will be different. i.e. Something about the light bulb limits the size of current flow in the circuit. The light bulb has some mpedance 8

MPEDANCE: What restricts the current flow? As charges move through a material they experience some opposition to their flow. The degree of difficulty of current flow is measured in terms of the mpedance of the material. f a current flows through a material when an EMF,, is applied to the ends of the material, then the material has an mpedance, Z, given by: Z or The S.. Unit of mpedance is the Ohms There are three basic circuit components which give rise to mpedance Z ESSTANCE () CAPACTANCE (C) Energy is dissipated in a esistor in the form of heat Energy is stored in a Capacitor in the form of an Electric field NDUCTANCE (L) Energy is stored in an inductor in the form of a Magnetic field For a pure resistive circuit: Z = 9

esistance and Ohm s Law Under normal circumstances, wires present some resistance to the motion of electrons. Ohm s law relates the voltage to the current: Ohm s Law: The current flowing through a conductor is directly proportional to the potential difference across the ends of a conductor. O (constant) Be careful Ohm s law is not a universal law and is only useful for certain materials (which include most metallic conductors). 0

Linear esistance f the graph of current as a function of applied EMF is Linear, then the resistance is a constant. Such conductors are said to obey Ohm s Law and are referred as OHMC Gradient Non-linear esistance f the graph of current as a function of applied EMF is non-linear, then the resistance varies with the applied EMF. Such resistors do not obey Ohm s Law (NON-OHMC) For such resistors, it is common to define the dynamic resistance at some desired EMF (at volt) Gradient at ε Gradient e.g. Thermistors, Diodes, light bulbs

esistance and Ohm s Law Solving for the resistance from Ohm s Law, we find: O The units of resistance, volts per ampere, are called Ohms: Two wires of the same length and diameter will have different resistances if they are made of different materials. This property of a material is called the resistivity,. The resistance,, of a wire of length, L, and cross-sectional area, A, is given by: 2

esistance and Ohm s Law The difference between insulators, semiconductors, and conductors can be clearly seen in their resistivities: 3

esistance and Ohm s Law n general, the resistance of materials goes up as the temperature goes up, due to thermal effects. This property can be used in design of thermometers. esistivity decreases as the temperature decreases, but there is a certain class of materials called superconductors in which the resistivity drops suddenly to zero at a finite temperature, called the critical temperature T C. e.g. Mercury 4.2 K, Highest temperature at which Superconductivity has been observed is 25 K. 4

Exercise : Suppose a charge of 20 C drifts through a conductor of cross-sectional area, A, in 2.0 s. (i) Calculate the current through the conductor, (ii) How many electrons will pass through this conductor in.0 s to produce a current of 0A? Exercise 2: (i) How much current will flow through a lamp that has a resistance of 60 when connected across a 2 supply? (ii) What is the resistance of an electric frying pan that draws 2 A when connected to a 20 circuit? Exercise 3: For the circuit shown, find the current through and potential drop (voltage) across each resistor. 2 2 30 20 5

Energy and Power in Electric Circuits The potential difference,, between the ends of a wire is defined as the work (potential energy), dw, required to move a charge, dq, from one end of the wire to the other. i.e. Potential Difference = Work(Energy)/Charge Also, Current: dq dt dq dt du q dw dw q dq Power is defined as the rate at which the electrical energy is converted to heat, P = dw/dt P dw dt dq dt dq dt 2 2 f this Power is supplied for a time, t, then the amount of Energy converted to heat: Energy = Power Time E P t t 2 t S.. Units: Energy (Joules), J S.. Units: Power (Watts), W 2 t 6

When the electric company sends you a bill, your usage is quoted in kilowatt-hours (kwh). They are charging you for energy use, and kwh is a measure of energy. E P t Exercise 4: Calculate the power being dissipated in each resistor in the circuit Current flowing in the circuit: 20 50 0.4 A Power dissipated in the 0 : P 2 0.4 2 0.6 W Power dissipated in the 40 : P 2 0.4 2 40 6.4 W Total Power Dissipated: PT.6 6.4 8 W 7

esistors in Series and Parallel esistors connected end to end are said to be in series. They can be replaced by a single equivalent resistance without changing the current in the circuit. n series circuit, same current flows through each resistor 8

2-4 esistors in Series and Parallel Since the current through the series resistors must be the same in each, and the total potential difference is the sum of the potential differences across each resistor, eq 2 3 2 3... We find that the equivalent resistance is: 2 3 9

esistors in Series and Parallel esistors are in parallel when they are across the same potential difference; they can again be replaced by a single equivalent resistance: 20

2-4 esistors in Series and Parallel Using the fact that the potential difference across each resistor is the same, and the total current is the sum of the currents in each resistor,... We find: 2 3 eq eq 2 3 2... 2 3 3 Note that this equation gives you the inverse of the resistance, not the resistance itself! f just two resistors in parallel, then: Product Sum 2 eq 2 2

esistors in Series and Parallel f a circuit is more complex, start with combinations of resistors that are either purely in series or in parallel. eplace these with their equivalent resistances; as you go on you will be able to replace more and more of them. 22

EXAMPLE : Find the equivalent resistance between points A and B Solution: CED = 4+ 2 = 6 CD = 2 CD 6 3 6 2 2 AB = 8 23

EXAMPLE 2: Find the equivalent resistance between points A and B of the circuit shown if each resistor is 2 y Solution: To simplify the problem let us label each resistor a, b, c, d, e, and f. n.b. The resistors a and b are in series and the combination is in parallel with resistor c. The resultant of abc is in series with e. xyz = 2+ 2 = 4 x d u a c f b z e v xz = 4 2/4+2 = 8/6 xzv = 8/6 + 2 = 20/6 xuv = 2 + 2 = 4 xv = (20/6 4)/((20/6)+ 4) =.8 24

Exercise 5: Consider the circuit shown with three resistors, = 250.0, 2 = 50.0 and 3 = 350.0 connected in parallel to a 24.0 battery. Find: (i) the current supplied by the battery, (ii) the current through each resistor. Exercise 6: An electric heater draws a steady 5.0 A from a 20 line. (i) How much power does it require to operate? and (ii) How much does it cost per month (30 days) if it operates for 3.0 hours per day and the electricity company charges 9.2 cents per kwh? 25