Ch 191 Chapter 19 DC Circuits © 2006, B.J. Lieb Some figures electronically reproduced by permission of Pearson Education, Inc., Upper Saddle River, New Jersey Giancoli, PHYSICS,6/E © 2004.

Ch 192 EMF Devices that supply energy to an electric circuit are referred to as a source of electromotive force. Since this name is misleading, we just refer to them as source of emf (symbolized by  and a slightly different symbol in the book.) Sources of emf such as batteries often have resistance which is referred to as internal resistance.

Ch 193 Terminal Voltage r  ab V ab We can treat a battery as a source of  in series with an internal resistor r. When there is no current then the terminal voltage is V ab =  But with current I we have: The internal resistance is small but increases with age.

Ch 194 Circuit Symbols

Ch 195 Resistors in Series - Derivation We want to find the single resistance R eq that has the same effect as the three resistors R 1, R 2, and R 3. Note that the current I is the same throughout the circuit since charge can’t accumulate anywhere. V is the voltage across the battery and also V = V 1 + V 2 + V 3 Since V 1 = I R 1 etc., we can say The equivalent equation is V=IR eq and thus

Ch 196 Summary - Resistors in Series The current I is the same throughout the circuit since charge can’t accumulate anywhere.

Ch 197 Resistors in Parallel - Derivation This is called a parallel circuit Notice V 1 = V 2 = V 3 = V Since charge can’t disappear, we can say We can combine these equations with V = IR eq to give

Ch 198 Summary - Resistors in Parallel The electric potential (voltage) is the same across each resistor V 1 = V 2 = V 3 The current through the battery splits several ways I = I 1 + I 2 + I 3 Can be 2, 3 or more resistors in parallel.

Ch 199 Example 19-1A. A 3.0 V battery is connected to three resistors as shown. Calculate the resistance of the equivalent circuit and the power dissipated in the equivalent circuit. R 1 = 500 Ω, R 2 = 1000 Ω and R 3 = 2000 Ω.

Ch 1910 Example 19-1B Calculate the current and the power dissipated in each resistor and the total power dissipated in the circuit.

Ch 1911 Example A 3.0 V battery is connected to 4 resistors as shown. Calculate the resistance of the equivalent circuit and the current in the equivalent circuit. R1 = 500 Ω, R2 = 1000 Ω, R3 = 1000 Ω, and R4 = 2000 Ω.

Ch 1912 Ammeter To measure current ammeter must be in circuit. Must have small internal resistance or it will reduce current and give a faulty measurement.

Ch 1913 Voltmeters To measure voltage difference, it must be connected to two different parts of circuit. Must have high internal resistance or it will draw too much current which reduces voltage difference and gives a faulty measurement.

Ch 1914 Kirchhoff’s Junction Rule Kirchhoff’s Rules are necessary for complicated circuits. Junction rule is based on conservation of charge. Junction Rule: at any junction, the sum of all currents entering the junction must equal the sum of all currents leaving the junction. I3I3 I2I2 22 I1I1 11 a b R1R1 R2R2 R3R3 Point a: I 1 + I 2 = I 3 Point b: I 3 = I 1 + I 2

Ch 1915 Kirchhoff’s Loop Rule Loop rule is based on conservation of energy. Loop Rule: the sum of the changes in potential around any closed path of a circuit must be zero. I3I3 I2I2 22 I1I1 11 a b R1R1 R2R2 R3R3 All loops clockwise: Upper Loop: +  2 – I 2 R 3 – I 3 R 1 – I 3 R 2 = 0 Lower Loop: +  1 + I 2 R 3 –  2 = 0 Large Loop: +  1 – I 3 R 1 – I 3 R 2 = 0

Ch 1916 Using Kirchhoff’s Rules Current: Current is the same between junctions. Assign direction to current arbitrarily. If result is a negative current, it means that the current actually flows in the opposite direction. Don’t change direction, just give negative answer. Branches with a capacitor have zero current. Signs for Loop Rule Go around loop clockwise or counterclockwise. IR drop across resistor is negative if you are moving in direction of the current. Voltage drop across battery or other emf is positive if you move from minus to plus. Simultaneous Equations You will need one equation for each unknown. It pays to generate “extra” equations because they may lead to a simpler solution.

Ch 1917

Ch 1918 Continued

Ch 1919 Capacitors in Parallel V is the same for each capacitor The total charge that leaves the battery is Q = Q 1 + Q 2 + Q 3 = C 1 V + C 2 V + C 3 V Combine this with Q = C eq V to give:

Ch 1920 Capacitors in Series The charge on each capacitor must be the same. Thus Q = C 1 V 1 = C 2 V 2 = C 3 V 3 Combine this with V = V 1 + V 2 + V 3 to give:

Ch 1921 Charging a Capacitor (Qualitative) When switch is closed, current flows because capacitor is charging As capacitor becomes charged, the current slows because the voltage across the resistor is  - V c and V c gradually approaches . Once capacitor is charged the current is zero.

Ch 1922 RC Decay If a capacitor is charged and the switch is closed, then current flows and the voltage on the capacitor gradually decreases. Since I  V C we can say that: It is necessary to use calculus to find:

Ch 1923 Exponential Decay The value  = RC is called the time constant of the decay. If R is in  and C is in F, then  has units of seconds. During each time constant, the voltage falls to 0.37 of its value at the start of the period. We can also define the half-life (  1/2 ) by  1/2 = RC. During each half-life, the voltage falls to ½ of its value at the start of the period.

Ch 1924 Example 4

Ch 1925 Example 4 Continued

Ch 1926 Electric Hazards A current greater than  70 mA through the upper torso can be lethal. Wet skin: I = 120 V / 1000  = 120 mA Dry skin: I = 120 V /  = 12 mA Your body can act as a capacitor in parallel with the resistance and this gives greater current for ac.

Ch 1927 Electric Hazards The key to safety is don’t let your body become part of the circuit. Standing in water can give path to ground which will complete circuit. Bathrooms can be dangerous

Ch 1928 Grounded Enclosures Metal cabinet grounded by 3-prong plug protects if there is loose wire inside because it causes short that trips circuit breaker. “Ground fault detector” should turn off current in time to protect you Circuit Breakers are to slow for personal safety