Transient Currents Flashcards
Explain capacitor charging in a resistor-capacitor circuit.
The instant the circuit is switched on there will be no charge in the capacitor and current will equal V/R. As time passes the capacitor will charge creating a voltage that opposes the source voltage. I=(V-vc)/R
After 5 RC seconds the vc will equal source voltage and there will be no current flow.
What factors affect the charging time of a capacitive circuit (time constant)
The time constant (τ) is the amount of time needed for the voltage from a capacitor in a resistor capacitor circuit to be charged up to a given percentage of the input voltage. It is determined by the capacitance value (farads) and the resistance of the circuit. High resistance and capacitance will mean longer charging times.
τ = CR
Voltage from the capacitor (vc) will always reach 63.2% of V in CR seconds.
A capacitor will reach steady state in about 5 × CR seconds
Explain time constants of capacitative discharge
Capacitors discharge in a pattern of exponential decay. A fully charged capacitor will discharge to (100-63.2 = 36.8 %) of Vs in τ (RC) seconds. In theory it takes forever to fully discharge but in practice a vc is close enough to zero for practical purposes after 5RC seconds.
What is the formula for induced emf
E = -L ∆i/∆t E is emf measured in volts L is inductance measured in henrys i is current t is time The negative sign is because the induced emf will always oppose the current
What are henries used to measure
The inductance of a given inductor coil. This is determined by
-The number of turns of wire in the coil
-The material of the core
-The shape and size of the core
-The shape size and material of wires making up the coil
There is no precise formula for calculating inductance.
What is the relationship between current, voltage and time in a purely inductive circuit.
i = t V/L
Current equals time × voltage/ inductance
When the voltage is first applied the induced emf will oppose the source voltage. It will reach a steady state after 5L/C seconds.
What is the relationship between source voltage and induced emf in a purely inductive DC circuit.
When the current is increasing the induced emf will oppose the source voltage.
V= -Emf
The induced EMF can never be greater than the source voltage. When the current is decreasing the induced emf will try to maintain the source voltage.
Explain time constants of capacitative discharge
Capacitors discharge in a pattern of exponential decay. A fully charged capacitor will discharge to (100-63.2 = 36.8 %) of Vs in τ (RC) seconds. In theory it takes forever to fully discharge but in practice a vc is close enough to zero for practical purposes after 5RC seconds.
What is the difference between the time constant in an inductive and resistive circuit
In a capacitive circuit the time constant is τ=CR
In an inductive circuit τ= L/R
More resistance will increase the time constant in a capacitive circuit and decrease it in an inductive circuit
What is the difference between how inductors and capacitors store energy.
An inductor stores energy in a magnetic field
A capacitor stores energy in an electric field
Explain voltage across an inductor in a DC circuit
V = L ∆i/∆t
There is only a voltage across the inductor if the current is changing.
In the steady state phase there is zero voltage across a perfect inductor. In reality no inductor is perfect and thus every inductor has some resistance.
Explain how you calculate the current though an inductor in a DC circuit if you know the voltage and the inductance.
Voltage across an inductor is a derivative of current with respect to time. Hence current is an integral of voltage with respect to time.
