The current that flows is determined by the potential difference across the conductor and the resistance of the conductor (Ohm s law): V = IR P = VI

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1 PHYS1000 DC electric circuits 1 Electric circuits Electric current Charge can move freely in a conductor if an electric field is present; the moving charge is an electric current (SI unit is the ampere (A), often shortened to amps). We use the potential difference or voltage across the conductor to characterize the electric field (since V = E x) The current that flows is determined by the potential difference across the conductor and the resistance of the conductor (Ohm s law): The SI unit of resistance is the ohm (Ω). As current flows through a resistance, energy is lost: V = IR P = VI If the current is constant (which also means it doesn t change direction), the current is called a direct current or DC. What is an electric circuit? To maintain a steady electric current, the moving charge needs to be able to return to its starting location a complete circuit must be present. Since energy lost as the charge moves, this energy must be replaced by a power supply. The main ways to produce an electric current are generators using electromagnetic induction, and chemical batteries. The exact type of power supply is not important, how much energy is supplied is. We measure this energy by the potential difference provided by the power supply also called the voltage of the power supply. Note that the potential difference across a resistance is a potential drop, or a reduction in energy. The potential difference across a power supply is a potential rise a gain in energy. For a steady current, if we go around a complete circuit, the total energy supplied is equal to the total energy lost: V supply = V losses Usually, a simple circuit will only contain a single power supply. positive, and all potential drops negative, we can write: If we make all potential rises V = 0 around any closed circuit.

2 PHYS1000 DC electric circuits 2 Circuit diagrams An easy way to describe an electric circuit is with a circuit diagram a drawing showing the circuit. Standard symbols are used for the various components in the circuit, and the conductors (wires) joining them together are drawn as lines. Circuit symbols: power supply A DC power supply can be drawn in a number of different ways (we ll use the one on the left): +9 V + 9 V Resistors If the resistance of a component of an electric circuit is its main electrical property, we can call it a resistor. Why do we want to add resistance to a circuit? A component might perform some useful function, but its main electrical property is resistance we can represent it with a resistor. (For example, a heating element, or a light bulb.) We can use a resistor to control the current in a circuit. Once we put a resistor in a circuit, its resistance is so much larger than the resistance of the wires in the circuit, and we can assume that the resistance of the wires is zero. Circuit symbols: resistor Example: a 1.0 kω resistor connected to a 12 V power supply: 12 V 1.0 kω

3 PHYS1000 DC electric circuits 3 Series & parallel circuits Multiple components in a circuit can either be connected in series with each other R R 1 2 R3 in parallel with each other R 1 R 2 R 3 Series circuits Example: a 1.0 kω and a 2.0 kω resistor connected in series with a 12 V power supply: 12 V 1.0 kω 2.0 kω Note that as the current flows from A to B, power is lost in each resistor, so V AB = V 1 + V 2

4 PHYS1000 DC electric circuits 4 the same current flows through all the resistors the combined resistance of both resistors is I A = I 1 = I 2 = I B R T = R 1 + R 2 Example: a 1.0 kω and a 2.0 kω resistor connected in parallel with a 12 V power supply: 12 V 1.0 kω 2.0 kω Note that all the resistors connect the same two points in the circuit together, so they must all have the same potential difference across them V AB = V 1 = V 2 the current at A splits up to flow through all of the resistors the combined resistance of both resistors is I A = I 1 + I 2 = I B 1 R T = 1 R R 2 Measuring currents and voltages We use ammeters and voltmeters to measure current and potential difference. ammeter The current to be measured must flow through the meter connect in series A

5 PHYS1000 DC electric circuits 5 voltmeter We want to measure the potential difference across two points connect in parallel across these two points V A B A multimeter is a convenient device that can measure either voltage or current (and resistance as well). Capacitors ADVANCED Two parallel plates with positive and negative charges equal in magnitude can be used to store electrical energy. This is called a capacitor. This energy can be used as a power supply in a circuit. The stored energy depends on the charge and the capacitance (measured in farads (F)). Q = CV Since the potential difference between the two plates depends on the charge on the plates, the voltage across the capacitor will fall as current flows from it as the capacitor discharges. How quickly the voltage falls depends on how much current flows, which depends on the resistance in the circuit. V = V 0 exp t/rc where R is the resistance in the circuit and C is the capacitance of the capacitor. The quantity RC is called the time constant, and is usually written as τ. Similarly, it takes time to charge a capacitor: This can be used to measure time in DC circuits. V = V 0 (1 exp t/τ) When the capacitor is fully charged or discharged, no current will flow. Circuit symbols: capacitor

6 PHYS1000 DC electric circuits 6 AC circuits EXTRA Another common type of electric current is alternating current, or AC. In an AC circuit, the current varies sinusoidally, and flows first in one direction, and then the other. If a suitable average voltage and current are used for AC, Ohm s Law can still be used for circuits which only contain resistors.

Tutorial 12 Solutions

Tutorial 12 Solutions PHYS000 Tutorial 2 solutions Tutorial 2 Solutions. Two resistors, of 00 Ω and 200 Ω, are connected in series to a 6.0 V DC power supply. (a) Draw a circuit diagram. 6 V 00 Ω 200 Ω (b) What is the total