(32.9) We have only been discussing DC circuits so far. However, using a capacitor we can create an RC circuit. In this example, a capacitor is charged but the switch is open, meaning no current flows. Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 1 / 1
(32.9) We have only been discussing DC circuits so far. However, using a capacitor we can create an RC circuit. Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 1 / 1
(32.9) We have only been discussing DC circuits so far. However, using a capacitor we can create an RC circuit. In this example, a capacitor is charged but the switch is open, meaning no current flows. The switch closes and current flows through the resistor, discharging the capacitor. The current stops once the capacitor is discharged. Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 1 / 1
(32.9) We have only been discussing DC circuits so far. However, using a capacitor we can create an RC circuit. In this example, a capacitor is charged but the switch is open, meaning no current flows. The switch closes and current flows through the resistor, discharging the capacitor. The current stops once the capacitor is discharged. The voltage around the loop is V C + V R = C IR = 0 Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 1 / 1
The rate of charge leaving the capacitor is equal to the rate of charge passing through the circuit (the current) I = d Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 2 / 1
The rate of charge leaving the capacitor is equal to the rate of charge passing through the circuit (the current) I = d The loop then becomes (dividing by R and rearranging) C IR = 0 Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 2 / 1
The rate of charge leaving the capacitor is equal to the rate of charge passing through the circuit (the current) I = d The loop then becomes (dividing by R and rearranging) C IR = 0 Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 2 / 1
The rate of charge leaving the capacitor is equal to the rate of charge passing through the circuit (the current) I = d The loop then becomes (dividing by R and rearranging) C IR = 0 C + d R = 0 Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 2 / 1
The rate of charge leaving the capacitor is equal to the rate of charge passing through the circuit (the current) I = d The loop then becomes (dividing by R and rearranging) C IR = 0 C + d R = 0 RC + d = 0 Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 2 / 1
The rate of charge leaving the capacitor is equal to the rate of charge passing through the circuit (the current) I = d The loop then becomes (dividing by R and rearranging) C IR = 0 C + d R = 0 RC + d = 0 d = 1 RC We can solve this by integrating it. Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 2 / 1
The integral is 0 d = 1 t RC 0 Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 3 / 1
The integral is 0 d = 1 t RC 0 We can do that integral ln 0 = ln ln 0 = ln 0 = t RC Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 3 / 1
The integral is 0 d = 1 t RC 0 We can do that integral ln 0 = ln ln 0 = ln Solving for gives 0 = 0 e t/rc = 0 e t/τ where τ = RC is the time constant of the circuit. = t RC Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 3 / 1
The integral is 0 d = 1 t RC 0 We can do that integral ln 0 = ln ln 0 = ln Solving for gives 0 = 0 e t/rc = 0 e t/τ where τ = RC is the time constant of the circuit. The resistor current is then I = d = 0 τ e t/τ = 0 RC e t/τ = V C R = t RC e t/τ = I 0 e t/τ Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 3 / 1
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 4 / 1
Charging a Capacitor Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 5 / 1