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Electrical Energy And Power, And Emf Dr Miguel Cavero August 7, 2014 Energy And Power, And Emf August 7, 2014 1 / 20 Energy Consider a component in a circuit with a potential difference ∆V across it and a current I through it. There is work done (q∆V ) on the charge by the electric field. The potential energy of a positive charge decreases as it moves through the component (the charge ”falls” from a point of higher potential to a point of lower potential). Does the charge gain kinetic energy? Energy And Power, And Emf Electrical Energy And Power August 7, 2014 3 / 20 Energy Consider a component in a circuit with a potential difference ∆V across it and a current I through it. The current - which is the rate of flow of charge ∆q/∆t - entering the component must be the same as the current leaving it. The energy q∆V is transferred to the circuit component. Energy And Power, And Emf Electrical Energy And Power August 7, 2014 4 / 20 Energy What happens if the potential difference across the component is negative? In this case, there is a net transfer of energy out of the component. The component acts as a source, delivering electrical energy to a circuit. Energy And Power, And Emf Electrical Energy And Power August 7, 2014 5 / 20 Energy When electrical energy is transferred to a component, that component is referred to as a load. The load in a circuit converts electrical energy into other forms. A load might be a resistor, that converts electrical energy into thermal energy (like the coils in a toaster), or a motor, that converts electrical energy into mechanical energy (to do work). When electrical energy is transferred out of a component, that component is referred to as a source. A battery is an example of a source. It converts chemical energy into electrical energy, which is available to the circuit the source is connected to. Energy And Power, And Emf Electrical Energy And Power August 7, 2014 6 / 20 Rate Of Change Of Energy Recall from mechanics, that power P is defined as the (time) rate of work done: W P = ∆t The work done W on charges moving through a component is q∆V is equal to the energy transferred into/out of the component. The power (the rate of energy transferred into/out of the component) is P q∆V ∆t = ∆V I = The SI unit of power is the watt, W (1 W = 1 V A = 1 J C−1 × 1 C s−1 ). Energy And Power, And Emf Electrical Energy And Power August 7, 2014 7 / 20 Power In A Resistor In the case where the load is a resistor, the potential difference across the resistor R is given by Ohm’s Law ∆V = IR where I is the current through the resistor. The electrical power delivered to the resistor is P = ∆V I = (IR)I = I 2 R ∆V (∆V )2 = ∆V = R R Energy And Power, And Emf Power Into A Pure Resistor August 7, 2014 9 / 20 The Kilowatt-Hour Electricity is generally measured and charged for in terms of electrical energy. The kilowatt-hour (kWh) is defined as the total work done in one hour when the power is 1 kW = 1000 W. 1 kWh = 1000 W × 3600 s = 3.6 × 106 J = 3.6 MJ Note: the kilowatt-hour is a unit of energy (or work) and not power. Energy And Power, And Emf Commercial Unit Of Electrical Energy August 7, 2014 11 / 20 Steady Current For an electrical component (such as a resistor) to have a steady current, it must be part of a complete circuit, sometimes referred to a closed loop. There can be no steady motion of charge in an isolated electrical component. To maintain a steady current in a (complete) circuit, charge carriers need electric potential energy to complete one loop of the circuit. Consider a fountain in a garden. At the point where the water comes out, it has gravitational potential energy compared to the ground, so the water falls before collecting in a pool at the bottom. A pump then increases the potential energy of the water to repeat the process. Energy And Power, And Emf Emf August 7, 2014 13 / 20 Electric Potential Energy Consider a simple circuit of three resistors in series. The electric potential drops across each of the resistors. The potential energy for any (positive) charge decreases as it moves through the circuit. Energy And Power, And Emf Emf August 7, 2014 14 / 20 Electric Potential Energy For the charge to move around the circuit again, it must gain potential energy from somewhere. Energy And Power, And Emf Emf August 7, 2014 15 / 20 Emf A device that increases the potential energy of a charge in a circuit is referred to a source of emf. An example is a battery. The emf, denoted by E, is like a charge ”pump” - moving a positive from a point of low electric potential to a point of higher electric potential. Note that an emf is not a force. An emf is a work per unit charge, so it is dimensionally the same as an electric potential. The SI unit of an emf is the volt, V. A battery that has an emf of 1.5 V does 1.5 J of work on every qaunity of charge of 1 C that passes through it. Energy And Power, And Emf Emf August 7, 2014 16 / 20 Emf The circuit could look like this: Conventional current direction means that the current moves in a clockwise manner in this circuit, from the positive terminal (the high-potential side) to the negative terminal (low-potential side). Energy And Power, And Emf Emf August 7, 2014 17 / 20 An Example In the circuit above, the battery has an emf of E = 12 V and the value of the three resistors are as follows: R1 = 2 Ω, R2 = 1 Ω and R3 = 3 Ω. What is the current flowing in the circuit? The current I is: 12 E I= = = 2A Req 6 Energy And Power, And Emf Emf August 7, 2014 18 / 20 An Example In the circuit above, the battery has an emf of E = 12 V and the value of the three resistors are as follows: R1 = 2 Ω, R2 = 1 Ω and R3 = 3 Ω. What is the potential difference across R3 , the 3 Ω resistor? The potential difference ∆V3 across R3 is: ∆V3 = IR3 = 2 × 3 = 6 V Energy And Power, And Emf Emf August 7, 2014 19 / 20 An Example In the circuit above, the battery has an emf of E = 12 V and the value of the three resistors are as follows: R1 = 2 Ω, R2 = 1 Ω and R3 = 3 Ω. What is the power delivered to R3 ? P = ∆V3 I = I 2 R3 = Energy And Power, And Emf (∆V3 )2 = 6 × 2 = 12 W R3 Emf August 7, 2014 20 / 20