Chapter 20 Circuit Elements (capacitor, resistor, and Ohm’s law)

Capacitance A capacitor is a device used in a variety of electric circuits A capacitor is a device used in a variety of electric circuits The capacitance, C, of a capacitor is defined as the ratio of the magnitude of the charge on either conductor (plate) to the magnitude of the potential difference between the conductors (plates) The capacitance, C, of a capacitor is defined as the ratio of the magnitude of the charge on either conductor (plate) to the magnitude of the potential difference between the conductors (plates)

Capacitor A Any two conductors separated by an insulator: capacitor d C =  o A/d  o = 8.85x F/m Q =C V [C] = C/V = Farad C

Parallel-Plate Capacitor The capacitance of a device depends on the geometric arrangement of the conductors The capacitance of a device depends on the geometric arrangement of the conductors For a parallel-plate capacitor whose plates are separated by air: For a parallel-plate capacitor whose plates are separated by air:  o = 8.85x F/m

 - +Q -Q  Q Q = C  Capacitanc e

Parallel connection Series connection C1C1 C2C2 C3C3 C1C1 C2C2 C3C3 C eq = C 1 + C 2 + C 3 1/C eq = 1/C 1 +1/C 2 +1/C 3

C eq

Example Three capacitors C 1 =1F, C 2 =2 F, C 3 =6 F. Find capacitance of the equivalent capacitor. C eq

Applications of Capacitors – Camera Flash The flash attachment on a camera uses a capacitor The flash attachment on a camera uses a capacitor A battery is used to charge the capacitorA battery is used to charge the capacitor The energy stored in the capacitor is released when the button is pushed to take a pictureThe energy stored in the capacitor is released when the button is pushed to take a picture The charge is delivered very quickly, illuminating the subject when more light is neededThe charge is delivered very quickly, illuminating the subject when more light is needed

Applications of Capacitors -- Computers Computers use capacitors in many ways Computers use capacitors in many ways Some keyboards use capacitors at the bases of the keysSome keyboards use capacitors at the bases of the keys When the key is pressed, the capacitor spacing decreases and the capacitance increasesWhen the key is pressed, the capacitor spacing decreases and the capacitance increases The key is recognized by the change in capacitanceThe key is recognized by the change in capacitance

H-ITT remotes You can buy the remotes from most bookstores. Buy only the H-ITT remotes, no Turning point remotes. You can buy the remotes from most bookstores. Buy only the H-ITT remotes, no Turning point remotes. Register remotes (if you got an with the score then you are ok). Register remotes (if you got an with the score then you are ok). Tune remotes Tune remotes Answer the questions in class Answer the questions in class Look for your registration number on the screen. In subsequent classes your number will appear in the same spot. Look for your registration number on the screen. In subsequent classes your number will appear in the same spot. You have 4 attempts. You have 4 attempts. Check your for quiz scores Check your for quiz scores

A capacitor is designed so that one plate is large and the other is small. If the plates are connected to a battery, (a) the large plate has a greater charge than the small plate, (b) the large plate has less charge than the small plate, or (c) the plates have charges equal in magnitude but opposite in sign. QUICK QUIZ

QUICK QUIZ ANSWER (c). The battery moves negative charge from one plate and puts it on the other. The first plate is left with excess positive charge whose magnitude equals that of the negative charge moved to the other plate.

Electric Current Whenever electric charges of like signs move, an electric current is said to exist Whenever electric charges of like signs move, an electric current is said to exist The current is the rate at which the charge flows through the wire The current is the rate at which the charge flows through the wire The SI unit of current is Ampere (A) The SI unit of current is Ampere (A) 1 A = 1 C/s1 A = 1 C/s

Electric Current, cont The direction of current flow is the direction positive charge would flow The direction of current flow is the direction positive charge would flow This is known as conventional current flowThis is known as conventional current flow In a common conductor, such as copper, the current is due to the motion of the negatively charged electrons In a common conductor, such as copper, the current is due to the motion of the negatively charged electrons It is common to refer to a moving charge as a mobile charge carrier It is common to refer to a moving charge as a mobile charge carrier A charge carrier can be positive or negativeA charge carrier can be positive or negative

Current: amount of charge flowing through a point per unit time Current flows from higher potential to lower potential  I    = R I Ohm’s law R 

Example In a tv tube, 5 x electrons shoot out in 4 s. What is the electric current?

Resistance In a conductor, the voltage applied across the ends of the conductor is proportional to the current through the conductor In a conductor, the voltage applied across the ends of the conductor is proportional to the current through the conductor The constant of proportionality is the resistance of the conductor The constant of proportionality is the resistance of the conductor

Resistance, cont Units of resistance are ohms (Ω) Units of resistance are ohms (Ω) 1 Ω = 1 V / A1 Ω = 1 V / A Resistance in a circuit arises due to collisions between the electrons carrying the current with the fixed atoms inside the conductor Resistance in a circuit arises due to collisions between the electrons carrying the current with the fixed atoms inside the conductor

Ohm’s Law Experiments show that for many materials, including most metals, the resistance remains constant over a wide range of applied voltages or currents Experiments show that for many materials, including most metals, the resistance remains constant over a wide range of applied voltages or currents This statement has become known as Ohm’s Law This statement has become known as Ohm’s Law V = I RV = I R Ohm’s Law is an empirical relationship that is valid only for certain materials Ohm’s Law is an empirical relationship that is valid only for certain materials Materials that obey Ohm’s Law are said to be ohmicMaterials that obey Ohm’s Law are said to be ohmic

V = R I Resistance, R = V/I [R] = V/A =  Ohm  For a fixed potential difference across a resistor, the larger R, the smaller current passing through it. R eq

Parallel connection Series connection R1R1 R2R2 R3R3 R1R1 R2R2 R3R3 R eq = R 1 + R 2 + R 3 1/R eq = 1/R 1 +1/R 2 +1/R 3

Q2. What is the ratio of the current flowing through each resistor (I 1 :I 2 ) in the circuit? 1. 1:1 2. 3:1 3. 1:4 4. Need more info. 6 V R 1 = 10 R 2 = 30

Electrical wires can be bent and/or stretched. A Node point (branching point) can be moved arbitrarily along the wire.

There are n identical resistors connected in parallel. R eq ? 1/R eq = 1/R + 1/R + 1/R + … + 1/R = n/R R eq = R/n

RaRa RbRb (1) 1/R eq = 1/R a + 1/R b (2) R eq is smaller than R a and R b R eq ≈ = 1k 2 R eq < 2 Practically all the current flows Though the bottom one!!

Ohm’s law:  = R·I R 1 = 6 6 V I =  /R = (6 V)/(6 Ohm) = 1.0 A What is the electric potential at ? We cannot tell the absolute potential at this point. If  at is +6 V, then 0 V at If  at is +3 V, then -3 V at For both, the potential diff. is 6 V.

To be able to specify absolute potential at a given point, we need to specify a reference point “0” potential. GROUND R 1 = 6 6 V  = “0” Then,  at is +6 V.

R 1 = 6 6 V R 2 =4R 3 =2  = R 3 I = 2 (V)  = R 2 I = 4 (V)  = = 6 (V)  = 2 V