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Title : AC Circuits Apparatus : Science Workshop Interface 750 1 Voltage sensor ( PASCO CI-6503 ) 3 Variable Resistor ( 0 - 100 ohms ) 1 Inductors ( 240-turn coil with two soft-iron C-cores ) 1
Capacitors (
Objective : 1. Study the phase relationship between the applied voltage and the current in C, RC and RL circuits 2. Study how the phase relationship between the applied voltage and the current varies with frequency 3. Study the relationship between the peak voltage across each of the components of the circuit and the applied peak voltage 4. Study the phase relationship between the applied voltage and the current and the amplitude of the current in the RLC circuit during resonance
Theory : A.C. through a pure capacitance
The p.d. across the capacitor at time t is given by V = V o sin wt The charge Q on the capacitor at time t is Q = C V = C Vo sin wt The current I, in the circuit is equal to the rate of flow of charge
Writing Io = w C Vo gives
In
a purely capacitative circuit the applied p.d. lags the currents by The
reactance is defined by Substituting
Io = w C Vo gives A.C. through a pure inductance
Consider an inductor of inductance L and zero resistance connected across an alternating supply. ( An inductor which has zero resistance is called a pure inductance. ) An alternating current ( I = Io sin wt ) flows through the inductor and sets up a changing magnetic flux.
V – w L Io cos wt = 0 Writing Vo = w L Io Gives
In
a purely inductive circuit the applied p.d. leads the current by The
reactance is defined by Substituting
Vo = w L Io gives Resistance and capacitance in series circuit
Note : V, VR and VC are either the peak values or the r.m.s. values. In
a RC circuit the applied p.d. lags the current by Resistance and inductance in series circuit
Note : V, VR and VL are either the peak values or the r.m.s. values In
a RL circuit the applied p.d. leads the current by Resistance, capacitance and inductance in series circuitThe impedance Z of the RLC circuit is given by
At
a certain frequency, fo , called the resonant
frequency, XL = XC and Z has its minimum value,
being equal to R. The current I has a maximum value and the phase angle The applied p.d. and the current are in phase at resonance. Procedure : Hardware setup : 1. Connect the Interface to the Computer, turn on the interface, and turn on the computer. 2. Connect the Voltage Sensors to the interface 3. Connect the function generator ( OUTPUT ports on the interface ) directly across the C, L, RC, RL or RLC circuit Use the "Output" feature of the interface to supply a voltage to the circuit. Use the Voltage Sensors to measure the voltage across the resistor, capacitor and inductor Software setup : Phase relationship between V and I Software Setup Data Recording : Use a multimeter to measure the resistance of the inductor coil and the resistance of the resistor. Click the Record (REC) button to begin recording data. Data sampling would stop automatically.
Data Analysis : Phase relationship between the applied voltage and the current in A.C. circuits (i) A.C. through a pure capacitance (ii) A.C. through a pure inductance
How the phase relationship between V and I varies with resistance in (i) RL circuit Phase decreases as R increases (ii) RC circuit Phase decreases as R increases
How the phase relationship between V and I varies with frequency in (i) RC circuit Calculation of capacitance in RC circuit (ii) RL circuit Calculation of inductance in RL circuit (iii) RLC circuit Phase difference between V and I is zero at resonance The amplitude of the current in the RLC circuit is maximum at resonance
Discussion : 1. What are the precautions of this experiment ? 2. Discuss the sources of error in the above experiments. 3. In the calculation of inductance in RL circuit, which method is more reliable ?
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