Capacitors Parallel-plate Physics 132: Lecture e 7 Elements of Physics II Charging of capacitors Agenda for Today Combinations of capacitors Energy stored in a capacitor Dielectrics in capacitors Physics 201: Lecture 1, Pg 1
Clicker Question 1: Metal wires are attached to the terminals of a 3 V battery. What is the potential difference between points 1 and 2? A. 6V. B. 3 V. C. 0 V. D. Undefined. E. Not enough information to tell. If there is a potential difference, a charge will feel a force A conductor has roughly an infinite number of free charges Therefore, a conductor in equilibrium is an equipotential. Physics 201: Lecture 1, Pg 2
How Capacitor works When a voltage is applied over a capacitor it will become charged. Circuit is open, and there is no charge on capacitor Battery Physics 201: Lecture 1, Pg 3
How Capacitor works When circuit is closed and a voltage is applied capacitor quickly becomes charged. -Q V C = 12 V +Q Battery Potential difference is same as battery!! Electrons effectively y travel from one plate V B = 12 V to the other plate! Physics 201: Lecture 1, Pg 4
How Capacitor works What happens after capacitor is fully charged? No more charges flowing!!!! Charge is ready to be -Q +Q used Battery Student: Why is the electric potential ti difference between the capacitors the same as the battery? Physics 201: Lecture 1, Pg 5
How Capacitor works -Q +Q Battery Student: when the circuit is closed, is the light bulb just "blink"? or it will shine for a while? Can deliver energy faster than a battery Cannot hold as much energy as a similar-sized battery Physics 201: Lecture 1, Pg 6
Definition of Capacitance Capacitance: The ratio of the charge on one conductor to the potential difference between conductors C Q V Units: Farad (F) Capacity to hold charge The larger the capacitance, the more charge can be stored with a certain potential difference. Student: Does capacitor have similar role as resistance? Student: Is there any difference in using V or (delta)v for potential difference? (the textbook uses both from time to time) Physics 201: Lecture 1, Pg 7
Parallel Plate Capacitor Capacitance of PP can be found: ε0 8.85 10 12 2 C Nm 2 A is area of plate 0 is permittivity of free space d is distance of separation Plates with more area have bigger C!! Closer plates have bigger C!! C ε0 A d Physics 201: Lecture 1, Pg 8
How Capacitor works -Q +Q Battery Physics 201: Lecture 1, Pg 9
C ε0 How Capacitor works A 0 Closer plates = Larger E-field d -Q - +Q Battery Larger E-field = More Charge Physics 201: Lecture 1, Pg 10
Clicker Question 2: A parallel-plate capacitor initially has a voltage of 400 V and stays connected to the battery. If the plate spacing is now doubled, what happens? a) the voltage decreases b) the voltage increases c) the charge decreases 400V d) the charge increases e) both voltage and charge change C Physics 201: Lecture 1, Pg 11
Dielectrics in Capacitors Insulating sheets called dielectrics are sometimes placed between the plates of a capacitor This allows for the plates to be closer together thus having a larger capacitance (without electrons flowing between) So we get a new relation for the capacitance of PP when a dielectric is between the plates: A C κε 0 d is dielectric constant Physics 201: Lecture 1, Pg 12
Dielectrics in Capacitors Electric field when capacitor is charged When a dielectric is added it polarizes This makes an E-field that partially cancels the original E-field. Allows same charge to be held on the capacitor with smaller potential, thus capacitance is increased th t ti ll l th + + + - + + - + + + + - + + - + - + + - + - - - - - - + + - Student: If a battery remains attached to a capacitor with a dielectric in it, would the voltage still decrease? Physics 201: Lecture 1, Pg 13
Capacitors in Series and Parallel Physics 201: Lecture 1, Pg 14
Capacitors in Parallel -Q +Q 2 2 Total charge is increased! Potential difference is same for both! -Q 1 +Q 1 Battery C eq = C 1 + C 2 Two capacitors don t y effect ec each other Physics 201: Lecture 1, Pg 15
Capacitors in Series This time the capacitors will effect each other Potential difference of capacitors adds up to that of battery -Q +Q-Q +Q 1 C eq 1 C 1 1 C 2 Battery Charge must be equal Physics 201: Lecture 1, Pg 16
Summary: Capacitors in Series and Parallel C eq V Q Series V Q = Q eq = V 1 + V 2 1 2 Parallel C eq = C 1 + C 2 V 1 = V 2 Q eq = Q 1 + Q 2 Physics 201: Lecture 1, Pg 17
PCQ: Find the equivalent capacitance of these capacitors. Physics 201: Lecture 1, Pg 18
Clicker Question 3: Find the equivalent capacitance of these capacitors. (a) 10.4 F (b) 13 F (c) 4.44 F (d) 6 F (e) 12.4 F Physics 201: Lecture 1, Pg 19
Clicker Question 3: Find the equivalent capacitance of these capacitors. Physics 201: Lecture 1, Pg 20
Clicker Question 4/Example: What is the voltage across the 6 μf capacitor? (a) (b) (c) (d) (e) 10 V 12 V 18 V 20 V 30 V Physics 201: Lecture 1, Pg 21
Clicker Question 4/Example: What is the voltage across the 6 μf capacitor? C ( F) Q ( C) V (V) Physics 201: Lecture 1, Pg 22
Stored energy in a capacitor First electron: W = q V = q (0) U 1 2 Last electron: W = q V q V Average: W = 1/2 q V -Q +Q Battery QV Using Q = CV U = ½QV = ½CV 2 = ½Q 2 /C Physics 201: Lecture 1, Pg 23
Clicker Question 5: A parallel plate capacitor is charged by connecting it to a battery. The battery is then removed, leaving the charge on the capacitor plates. What happens to the energy stored in the capacitor when the plates are pulled a small distance further apart? (a) It decreases. (b) It stays the same (c) It increases. Physics 201: Lecture 1, Pg 24