RC Circuits Physics 102 Professor Lee Carkner Lecture 16
Series and Parallel V = 6 for each branch so I 2 = V/R = 6/6 = 1 A and I 3 = V/R = 6/10 = 0.6 A Equivalent resistance total: 1/R eq = 1/6 +1/10, R eq = 3.75 so I 1 = I eq = V/R eq = 6/3.75 = 1.6 A through battery ( V=6) + - V = 6 V 10 4 6 I1I1 I3I3 I2I2
Kirchhoff’s Rules Left loop: 6 - 6I 2 = 0 Right loop: 6I 2 - 6I 3 - 4I 3 = 0 I 1 = I 2 +I 3 Voltage: For battery V = 6 V, for 6 , V = 6I 2 = 6 V, for 2nd 6 , V = 6I 3 = 3.6 V, for 4 , V = 4I 3 = 2.4V + - V = 6 V 4 6 I1I1 I3I3 I2I2
Kirchhoff Tips Find the currents Each single branch has a current Indicate current direction Apply junction rule Currents in equal currents out
More Kirchhoff Tips Apply the loop rule Sum of all V equal to zero From - to + terminal the V is equal to + Moving with the current the V is - IR Solve equations Need as many equations as unknowns Check your work
Today’s PAL Use Kichhoff’s rules to find the current through each resistor
Capacitance The value of C depends on its physical properties: C = 0 A/d How can we combine capacitors in circuits?
Simple Circuit Battery ( V) connected to capacitor (C) The capacitor experiences potential difference of V and has stored charge of Q = C V VV C Q
Capacitors in Parallel Potential difference across each is the same ( V) But: Q 2 = C 2 V The equivalent capacitance is: C eq = C 1 + C 2 +- VV C1C1 C2C2
Capacitors in Series Charge stored by each is the same (Q) Equivalent capacitor also has a charge of Q Since V = Q/C: The equivalent capacitance is: 1/C eq = 1/C 1 + 1/C 2 +- VV C1C1 C2C
Capacitors in Circuits Remember series and parallel rules extend to any number of capacitors Keep simplifying until you find the equivalent capacitance for the whole circuit
Resistors and Capacitors If you add a resistor to a charged capacitor, the capacitor will discharge through it If we charge a capacitor with a resistor in the circuit, it will also take time for the capacitor to fully charge = RC This is the time to charge a capacitor to about 63% of the final value
Charging a Capacitor
Charge on the Capacitor We can write an expression for the charge on a capacitor: Q(t) = C [1-e (-t/ ) ] Capacitor charges rapidly at first and then the rate of charge separation slows At about t = 4 the capacitor is nearly fully charged
Time Curve
Meters We use meters to measure current, resistance, capacitance, voltage, etc. Want to minimize their effect
Using an Ammeter
Using a Voltmeter
Types of Meters Ammeter Must be placed in series Voltmeter Must be placed in parallel
Next Time Read Homework Ch 21, P: 29, Ch 22, P: 2 Final: Section 1: Tuesday, Feb 25, 9-11 am Section 2: Thursday, Feb 27, Noon-2pm