# Circuit Report

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• Published: March 30, 2006

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Objective

The aim of the experiment is to understand the properties of the passive elements and the resonance.

Apparatus

1. Unknown Box

2. Passive Elements: Resistors, Inductors and Capacitors

3. A.C. Power supply

4. Connecting Wires

5. Multimeter

Introductory Theory

Passive elements

Passive elements are elements that can either absorb energy or store energy.

There are 3 types of passive elements, which are shown below:

Resistor: A resistor is a two-terminal electrical or electronic component that resists an electric current by producing a voltage drop between its terminals in accordance with Ohm's law.

Inductor: An inductor is a passive electrical device employed in electrical circuits for its property of inductance. It stores energy in magnetic form.

Capacitor: A capacitor is a device that stores energy in the electric field created between a pair of conductors on which equal but opposite electric charges have been placed.

Black

It is a box which contains an unknown passive element other than a resistor. Both of them are connected in series.

Resonance

A circuit is said to be in resonance when its impedance is equal to its resistance. There are two types of resonant circuit: Series and Parallel.

2 types of resonant circuits are shown as the following:

Series Resonant Circuit: Passive elements are connected in series.

Parallel Resonant Circuit: Passive elements are connected in parallel.

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Experiment 1: Unknown Component

Aim

The blackcontains an unknown passive element other than a resistor and it is connected to a resistor in series. The objective is to find the unknown component in the black box.

Procedure:

1) The unknown box is connected in series with a resistor, R in the circuit.

2) An AC power supply is connected to the circuit.

3) The potential different is set to be 1V throughout the experiment.

4) A multimeter is connected across the unknown box to measure its potential difference, VZ.

5) The results are recorded in a table and a graph Z versus Frequency, f is plotted.

Results:

f(kHz) VR (volts) VZ (volts) Z (ohm)

1 0.848 0.532 62.73585

2 0.65 0.79 121.5385

3 0.486 0.886 182.3045

4 0.387 0.941 243.1525

5 0.31 0.951 306.7742

6 0.262 0.969 369.8473

7 0.224 0.965 430.8036

8 0.189 0.943 498.9418

9 0.165 0.93 563.6364

Table 1.

Figure 1. Graph of f vs. Z

f(kHz) VR (volts) VZ (volts) Z (ohm)

10 0.143 0.911 637.0629

20 0.031 0.534 1722.581

30 0.003 0.329 10966.67

40 0.001 0.269 26900

50 0.001 0.316 31600

60 0.001 0.395 39500

Table 2.

Figure 2. Graph of f vs. Z

Discussion

Graph 1

1. In the first graph, the line cuts the x-axis at 5 ohm. Based on , the 5 ohm represents r where r is the internal resistance of the inductor.

2. Based on the graph, Z ( ) is proportional to f (kHz). In other words, impedance increases as frequency increases. Therefore, the unknown component is an inductor. Inductive reactance, XL is given by .

Graph 2

1. In the second graph, the impedance is plotted against a higher range of frequency. As frequency is high, r is negligible.

2. |Z| = r2 +

Since r = 0,

|Z| =

Therefore

|Z| / f = 2 L

Since |Z| / f is the slope, therefore

Slope = 2 L

Therefore

L = (slope/2 ) Henry

Conclusion:

The unknown component is an inductor. The internal resistance, r at the inductor is 5 . When the frequency is higher, r is negligible. The inductance, L is 146H.

Resonance

A circuit is said to be in resonance when its impedance is equal to its resistance. There are two types of resonant circuit: Series and Parallel.

2 types of resonant circuits are shown in the following 2 experiments.

Experiment 2: Series Resonance

Aim

All the passive elements are connected in series. The aim of this experiment is to investigate the properties of series resonace.

Procedure:

1) The conductor, C, inductor, L and...