Technical Report
Experiment no 4
AC Ohm’s Law
Carandang, Carmela Geraldine M. Date Performed: Jan 28, 2013 ACT 2ndyear Date Submitted: Feb 4, 2013
Remarks:_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
Engr. C.D. Sanchez
Instructor
II. Theoretical Discussion
Alternating currents and voltages
Figure 1 shows the plot of alternating voltage and alternating current as a function of time in a circuit that has only a resistor and a source of alternating current — an ac generator.






Figure 1 Current and voltage from an ac source through a simple resistor.


Because the voltage and current reach their maximum values at the same time, they are in phase. Ohm's law and the previous expressions for power are valid for this circuit if the root mean square (rms) of the voltage and the rms of the current, sometimes called the effective value, are used. These relationships are




Ohm's law is expressed thus: VR = IR, where VR is the rms voltage across the resistor and I is the rms in the circuit. Resistorcapacitor circuits
A circuit with a resistor, a capacitor, and an ac generator is called an RC circuit. A capacitor is basically a set of conducting plates separated by an insulator; thus, a steady current cannot pass through the capacitor. A timevarying current can add or remove charges from the capacitor plates. A simple circuit for charging a capacitor is shown in Figure 2 .






Figure 2 An RC circuit for charging a capacitor.


Initially, at time t = 0, the switch (S) is open, and there is no charge on the capacitor. When the switch is closed, a current will pass through the resistor and charge the capacitor. The current will cease when voltage drop across the capacitor equals the potential of the battery (V). Once the capacitor reaches the maximum charge, the current will decrease to zero. The current is at maximum immediately after the switch is closed and decreases exponentially with time. The capacitive time constant (τ), the Greek letter tau) is the time for the charge to decay to 1/ eof its initial value, where e is the natural logarithm. A capacitor with a large time constant will change slowly. The capacitive time constant is τ = RC. From Kirchhoff's rules, the following expressions for the potential difference across the capacitor (VC) and the current (I) in the circuit are derived:




where V is the potential of the battery.
Resistorinductance circuits
A circuit with a resistor, an inductor, and an ac generator is an RL circuit. When the switch is closed in an RL circuit, a back emf is induced in the inductor coil. The current, therefore, takes time to reach its maximum value, and the time constant, called the inductive time constant, is given by 



The equations for the current as a function of time and for the potential across the inductor are 



A switch was used in the above discussions of RC and RL circuits for simplicity. Opening and closing a switch gives a response similar to that of an ac current. The RC and RL circuits are similar to each other because an increase in voltage yields a current that changes exponentially in each circuit, but the responses are different in other ways. These different behaviors, described below, lead to different responses in ac circuits. Reactance
Now consider an ac circuit consisting only of a capacitor and an ac generator. The plots of current and voltage across the capacitor as a function of time are shown in Figure 3 . The curves are not in phase as they were for the circuit of a resistor and an ac generator. (Refer to Figure 1 .) The curves indicate that, for a capacitor,...
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