Lec2 (1) PDF - Electrical Circuit Laboratory Experiment

Electrical Circuit Laboratory Lecturer: Dr. Basim Al-Qargholi Experiment No.2 R-C Ohms' SeriesLaw Circuit 1. Introduction...

Electrical Circuit Laboratory Lecturer: Dr. Basim Al-Qargholi Experiment No.2 R-C Ohms' SeriesLaw Circuit 1. Introduction A resistor-capacitor circuit (RC circuit), or RC filter, is an electrical circuit composed of a passive component (resistors and capacitors) driven by a voltage or current source. The RC circuit can be used as a low pass filter to remove the higher frequency signals. Allowing the low-frequency signals to pass, the signals measured across the capacitor and have frequencies higher than the cut-off frequency will be removed. The RC circuit can also be used as a high pass filter, If the resistor and capacitor are switched, in their position. And the output signal across the resistor can be measured. A high pass filter is used to pass the high-frequency signals and removes the low-frequency signals. 2. Objectives The experiment aims to study the electrical characteristics of an RC circuit in series. Also, to study the relation between the input frequency f and the circuit impedance XC. 3. Components ▪ Function generator. ▪ Oscilloscope. ▪ Digital Multimeter. ▪ Resistor. ▪ Connection wires. ▪ Capacitor. 4. Theory: When an ac voltage is applied to a resistor and a capacitor in series, as shown in Fig. 1, the capacitor will constantly charge and discharge as the input voltage (Vin) is constantly changing. 1 Al-Mustaqbal University College http://www.mustaqbal-college.edu.iq/ Reactance is a characteristic exhibited by capacitors and inductors in circuits with time- varying voltages and currents, such as common sinusoidal AC circuits. Like resistance, reactance opposes the flow of electric current and is measured in ohms. Capacitive reactance XC can be found by the equation: 1 𝑋𝐶 = (2) 2𝜋𝑓𝐶 Where f is the frequency of the applied voltage or current and C is the capacitance in farads. As with resistance, the capacitor reactance obeys Ohm’s law: 𝑉𝐶 𝑉𝐶 = 𝐼𝐶 𝑋𝐶 𝑜𝑟 𝑋𝐶 = (3, 4) 𝐼𝐶 If a sinusoidal voltage is applied across a purely resistive circuit, it produces a sine wave (sinusoidal) current. Both waveforms attain their peak values at the same time, and pass through zero at the same time. Voltage and current, in a purely resistive circuit, are therefore said to be "IN PHASE" with each other. Figure 2: illustrate that the voltage and current wave are in phase in purely resistive load In a purely capacitive circuit, the voltage and current waveforms are not in phase. Capacitance has the property of delaying changes in voltage. The applied voltage reaches steady state only after a time dictated by the time constant. In AC circuits voltage and 3 Al-Mustaqbal University College http://www.mustaqbal-college.edu.iq/ current are changing continuously, and in a purely capacitive AC circuit, the peak value of the voltage waveform occurs a quarter of a cycle after the peak value of the current. Therefore, a phase shift is occurring in the capacitor, the amount of phase shift between voltage and current is +90° for a purely capacitive circuit, with the current LEADING the voltage as shown in Fig. 3. The opposite phase shift to an inductive circuit. Figure 3: illustrate the voltage and current phase shift in a purely capacitive load In an RC circuit, a phase shift occurs as well between the voltage across the capacitor VC and the current I. As the circuit is a resistive-capacitive load, the current leads the voltage, as shown in Fig. 4. The phase shift can be calculated using equation 5. Figure 4: illustrate the voltage and current phase shift of a resistive-capacitive load. 4 Al-Mustaqbal University College http://www.mustaqbal-college.edu.iq/ By applying the Kirchhoff voltage law (The summation of the drop voltages across R and L equal to the input voltage Vin) to this circuit, we get: 𝑉𝑖𝑛 = 𝑉𝑅 + 𝑉𝐿 (2) Before drawing the phasor diagram of a series RL circuit, one should know the relationship between voltage and current in the case of resistor and inductor. In the case of the resistor R, the voltage and current are in the same phase, or we can say that the phase angle difference 𝜃 between voltage and current is zero. Figure 1: illustrate that the voltage and current wave are in phase in purely resistive load In the case of the inductor L, the voltage and current are not in phase. The voltage leads the current by 90°. This means the voltage reaches its maximum when the current attains the zero value. Figure 2: illustrate the voltage and current phase shift in a purely inductive load Inductor (also named as a choke) is basically a coil or loops of wire that are either wound around a hollow tube former (air cored) or wound around some ferromagnetic material like iron core to increase their inductive value (inductance). 2 Al-Mustaqbal University College http://www.mustaqbal-college.edu.iq/