Physics 212 Lecture 8, Physics 212 Lecture 8, Slide Slide 1 Physics 212 Physics 212 Lecture 8 Lecture 8 Today's Concept: Today's Concept: Capacitors Capacitors How does a capacitor behave in a circuit? How does a capacitor behave in a circuit? More circuit examples More circuit examples
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Physics 212 Lecture 8, Slide 1 Physics 212 Lecture 8 Today's Concept: Capacitors How does a capacitor behave in a circuit? More circuit examples.
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How does a capacitor behave in a circuit?How does a capacitor behave in a circuit?More circuit examplesMore circuit examples
Main Point 1
First, filling the region between the plates of a capacitor with a dielectric will increase its capacitance. In particular, the ratio of the capacitance when filled with dielectric to that when filled with air is equal to kappa , the dielectric constant of the material.
Second, the equivalent capacitance of two capacitors connected in parallel is equal to the sum of the individual capacitances. The voltage across each capacitor is the same and is the equivalent voltage of the combination. The equivalent charge of the combination is equal to the sum of the charges on the individual capacitors.
Third, the equivalent inverse capacitance of two capacitors connected in series is equal to the sum of the individual inverse capacitances. The charge across each capacitor is the same and is the equivalent charge of the combination. The equivalent voltage of the combination is equal to the sum of the voltages across the individual capacitors.
This “Q” really means that the battery has This “Q” really means that the battery has moved charge Q from one plate to the other,moved charge Q from one plate to the other,so that one plate holds +Q and the other -Q.so that one plate holds +Q and the other -Q.
A circuit consists of three unequal capacitors C1, C2, and C3 which are connected to a battery of voltage V0. The capacitance of C2 is twice that of C1. The capacitance of C3 is three times that of C1. The capacitors obtain charges Q1, Q2, and Q3.
Compare Q1, Q2, and Q3.A. Q1 > Q3 > Q2 B. Q1 > Q2 > Q3 C. Q1 > Q2 = Q3 D. Q1 = Q2 = Q3 E. Q1 < Q2 = Q3
Two identical parallel plate capacitors are given the same charge Q, after which they are disconnected from the battery. After C2 has been charged and disconnected, it is filled with a dielectric.
Compare the voltages of the two capacitors.A. V1 > V2 B. V1 = V2 C. V1 < V2
Compare the potential energy stored by the two capacitors.A. U1 > U2 B. U1 = U2 C. U1 < U2
Checkpoint 4cCheckpoint 4cTwo identical parallel plate capacitors are given the same charge Q, after which they are disconnected from the battery. After C2 has been charged and disconnected, it is filled with a dielectric.
A. The charges will flow so that the charge on C1 will become equal to the charge on C2.B. The charges will flow so that the energy stored in C1 will become equal to the energy stored in C2.
C. The charges will flow so that the potential difference across C1 will become the same as the potential difference across C2.D. No charges will flow. The charge on the capacitors will remain what it was before they were connected.
In pre-lecture 7 we calculated the work done to move charge Q from one In pre-lecture 7 we calculated the work done to move charge Q from one plate to another:plate to another:
Energy in a Capacitor (1/2 QV)Energy in a Capacitor (1/2 QV)