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Chapter 18 Kirchhoff Example RC Circuits

Lecture 25. Chapter 18 Kirchhoff Example RC Circuits. Wednesday 24 March 1999. Physics 112. 12 W. 1 W. b. e. a. I 2. I 0. 6 W. I 1. 12 V. +. 18 V. _. d. f. c. 1 W. +. _. Find the currents in each branch of this circuit.

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Chapter 18 Kirchhoff Example RC Circuits

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  1. Lecture 25 Chapter 18 Kirchhoff Example RC Circuits Wednesday 24 March 1999 Physics 112

  2. 12 W 1 W b e a I2 I0 6 W I1 12 V + 18 V _ d f c 1 W + _ Find the currents in each branch of this circuit. There are two junction points, so we can apply the junction ruleONCE. I0 = I1 + I2

  3. 12 W 1 W b e a 6 W 12 V + 18 V _ d f c 1 W + _ 3 How many possible loops are there? b c d a e f c d a b e f c b We have 3 unknowns, so we need 3 equations total. Therefore, we need use only 2 of the 3 equations provided by the loop rule. (The junction rule gave us 1 equation already!)

  4. 12 W 1 W b e a I2 I0 6 W I1 12 V + 18 V _ d f c 1 W + _ Let’s go around bcda first. -(6W) I1 + 18 V - (12W) I0 = 0 (12W) I0 + (6W) I1 = 18 V

  5. 12 W 1 W b e a I2 I0 6 W I1 12 V + 18 V _ d f c 1 W + _ Let’s go around efcb second. 12 V - (1W) I2 + (6W) I1 - (1W) I2 = 0 (2W) I2 - (6W) I1 = 12 V

  6. 12 W 1 W b e a I2 I0 6 W I1 12 V + 18 V _ d f c 1 W (2W) I0 + (1W) I1 = 3 V + _ (1W) I2 - (3W) I1 = 6 V I0 = I1 + I2 (12W) I0 + (6W) I1 = 18 V (2W) I2 - (6W) I1 = 12 V I0 = 2 A I1 = -1 A I3 = 3 A

  7. RC Circuits Not the Cola! So far in Chapter 18, we’ve looked at circuits in which the currents are constant. These circuits have involved only resistors and sources of EMF. What happens if we put a capacitor into one of these circuits?

  8. + R I V C _ If I start with an initially uncharged capacitor, what happens when I close the switch? Charge begins to build up on the capacitor. The more charge on the capacitor, the more work it takes to bring up the next bit of charge, the more slowly the capacitor will charge. When the capacitor is fully charged (i.e. Q = CV), the current will stop flowing.

  9. + R V C _ q Q=CV Q=0.632CV t t Charging a capacitor Q = final charge on C t = the time constant = R C

  10. Concept Quiz! RC Discharging

  11. R C,V0,Q0 Discharging a capacitor I start with a capacitor with charge Q0 on it. What happens when I close the switch this time? Charge begins to flow off the capacitor through the resistor. Current is proportional to the potential drop across the capacitor. The less charge on the capacitor, the smallerthevoltage drop, the smallerthecurrent. So I expect the magnitude of the current to decrease as the capacitor discharges, eventually reaching 0.

  12. R C I q Q0=CV0 Q=0.368CV0 t t Discharging a capacitor Q0 = initial charge on C t = the time constant = R C

  13. Units! You might be saying to yourself, “I have a hard time believing that R times C gives me units of time!” t = R C [t] = [R] [C] [t] = W F = (V/A) (C/V) = C/A = C/(C/s) Yup! [t] = seconds!

  14. + 100W 6V 2mf _ Question What is the initial current in this circuit after the switch is closed?

  15. + 100W 6V 2mf _ What is the final charge on the capacitor? What is the time constant for this circuit?

  16. + 100W 6V 2mf _ How long after the switch is closed does it take for the capacitor to become 90% charged? q = 0.9 Qf = 0.9 (12mC) = 10.8mC q(t) = Qf (1 - e-t/t) 0.9 = (1 -e-t/200ms) 0.1 =e-t/200ms Take the natural log of both sides...

  17. + 100W 6V 2mf _ ln (0.1) =ln(e-t/200ms) -2.3 = -t / 200ms t = 460 ms

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