Electric circuits, Current, and resistance (Chapter 22 and 23)

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Harold Goodwin
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1 Electric circuits, Current, and resistance (Chapter 22 and 23) Acknowledgements: Several Images and excerpts are taken from College Physics: A strategic approach, Pearson Education Inc

3 Current If electric charge (e.g. electron) moves, we will say an electric current, I, is set to exist. I + A An electric current, I, is the rate at which net charge ( Q) flows through a surface area A I Q = t Current s units = C/S and often written as A (Ampere) Electrons are actual current carriers in metals. They flow opposite to the direction of electric field or current Although current carriers (i.e., charges) could be + or -, the direction of current will be in the direction of a + charge flow (i.e., clockwise)

4 Current and Current density n = number of mobile charges per unit volume q = charge on each current carriers x = distance they move in a time interval t v d = speed (called drift velocity ) J = current density Drift velocity v d? I x = v t d + Q = ( na x) q = ( nav t) q I J d Q = = nqvd A t I = = nqvd A A

5 Multiple choice questions 1. The charge carriers in metals are A. electrons. B. positrons. C. protons. D. a mix of protons and electrons. 2. A battery is connected to a resistor. Increasing the resistance of the resistor will A. increase the current in the circuit. B. decrease the current in the circuit. C. not affect the current in the circuit. 3. A battery is connected to a resistor. As charge flows, the chemical energy of the battery is dissipated as A. current. B. voltage. C. charge. D. thermal energy.

6 Problem: The discharge of the electric eel can transfer a charge of 2.0 mc in a time of 2.0 ms. What current, in A, does this correspond to? Solution: Step 1: To solve a problem, note each and every quantities mentioned in your problem. In this problem Q = 2.0 x10-3 C Time = 2.0 x10-3 s Current =? Step 2: Identify relationship between these quantities Step 3: Rearrange your equation to find out the unknown quantity Add each and every numbers and compute. Warning: Calculator does what you ask for.if you insert wrong numbers or in a wrong manner, you will get a wrong answer!!! You must learn how to use your calculator properly I = Q/t = 2.0x10-3 C/2.0x10-3 s = 1A

7 Batteries The potential difference between the terminals of a battery, often called the terminal voltage is often called battery s electromotive force (emf) Wchem Vbat = = q ξ

8 Simple Circuits The current is determined by the potential difference and the resistance of the wire: I = V wire R battery

9 Ohm s law and resistance A current density J & the electric field E are established in a conductor when a potential difference (V b -V a ) is maintained across the conductor J = σe Ohm s Law σ is called electrical conductivity of the materials Ohmic materials: In these materials the ratio of J and E is a constant σ. In other words, it is J varies linearly with E Value of conductivity of the materials are different for different materials V = V V b V E = V = El l V J = σ E = σ l l V = I V = RI σ A l R = σ A a ρl R = A

10 Resistance & Resistivity The resistance of a wire depends on its dimensions (length L & Cross sectional area A) and the resistivity of its material. R = ρl A Every material has a characteristic resistivity that only depends on the properties and composition of the material. Value of resistivity of the materials are different for different materials resistivity of the metal increase as temperature increase resistivity of semiconductors and insulators decreases as temperature increases

11 Multiple choice A battery is connected to a wire, and makes a current in the wire. Which of the following changes would increase the current? (1) Increasing the length of the wire; (2) keeping the wire the same length, but making it thicker; (3) using a battery with a higher-rated voltage; (4) making the wire into a coil, but keeping its dimensions the same; (5) increasing the temperature of the wire. Problem 1: A. All of the above B. 1 and 5 C. 1, 4, and 5 D. 2 and 3 E. None of the above A wire has resistance of 21 ohm. It is melted down and from the same volume of metal a new wire is made, that is three times longer than the original one. What is the resistance of new wire Problem 2: The filament of a 100-W bulb carries a current of 0.83 A at the normal operating voltage of 120 V. A. What is the resistance of the filament? B. If the filament is made of tungsten wire of diameter mm, how long is the filament?

12 Power in Circuits

13 Energy and Power in Resistors

14 Multiple choice A resistor is connected to a 3.0 V battery; the power dissipated in the resistor is 1.0 W. The battery is traded for a 6.0 V battery. The power dissipated by the resistor is now A. 1.0 W B. 2.0 W C. 3.0 W D. 4.0 W Problem 1: An electric blanket has a wire that runs through the interior. A current causes energy to be dissipated in the wire, warming the blanket. A new, low-voltage electric blanket is rated to be used at 18 V. It dissipates a power of 82 W. What is the resistance of the wire that runs through the blanket?

15 Example Problem An electric blanket has a wire that runs through the interior. A current causes energy to be dissipated in the wire, warming the blanket. A new, low-voltage electric blanket is rated to be used at 18 V. It dissipates a power of 82 W. What is the resistance of the wire that runs through the blanket? Summary

16 Conservation of Current I = in I out

17 Multiple choice questions 1. Rank the bulbs in the following circuit according to their brightness, from brightest to dimmest. A. A > B = C > D B. A = B = C = D C. A = D > B = C D. B = C > A > D

18 Drawing Circuit Diagrams

19 Kirchhoff s Law I = in I out V = V = loop i 0

20 Using Kirchhoff s Laws

21 Multiple choice questions 1. The diagram below shows a segment of a circuit. What is the current in the 200Ω resistor? A. 0.5 A B. 1.0 A C. 1.5 A D. 2.0 A E. There is not enough information to decide. 2. The diagram below shows a circuit with two batteries and three resistors. What is the potential difference across the 200Ω resistor? A. 2.0 V B. 3.0 V C. 4.5 V D. 7.5 V E. There is not enough information to decide.

22 Series Resistors

23 Parallel Resistors

24 Problems 1. There is a current of 1.0 A in the circuit below. What is the resistance of the unknown circuit element? 2. What is the current out of the battery?

25 Analyzing Complex Circuits

26 Problems 1. In the circuit shown below: A. Rank in order, from most to least bright, the brightness of bulbs A D. Explain. B. Describe what, if anything, happens to the brightness of bulbs A, B, and D if bulb C is removed from its socket. Explain.

27 Problems In the circuit shown below: A. How much power is dissipated by the 12 Ω resistor? B. What is the value of the potential at points a, b, c, and d?

28 Battery and its internal resistance (r) As the charges passes through from to + terminal of the battery its potential energy increases The current in the circuit -Depends both external resistance to the battery -And its internal resistance I = ξ R + r Due to internal resistance of the battery, its potential decreases by Ir, wherein I is the current. Terminal voltage of the battery = V + -V - = ξ-ir Note: Terminal voltage may exceed the emf by an amount Ir when the current is opposite the emf as in the case of charging a battery with another source of emf. Power dissipated, P, in the load resistance R ξ ( R + r) 2 P 2 = I R = R 2

29 Problems: 1. Show that maximum power lost in the load resistor R occurs when R =r, i.e., when the value of load resistance matches the internal resistance of the battery.

AP Physics Electricity and Magnetism #4 Electrical Circuits, Kirchoff s Rules

Name Period AP Physics Electricity and Magnetism #4 Electrical Circuits, Kirchoff s Rules Dr. Campbell 1. Four 240 Ω light bulbs are connected in series. What is the total resistance of the circuit? What