ELECTRONICS

ELECTRONICS ASSIGNMENT

Electronics Assignment

Assessment Criteria 5

5.1 (1) (A). Draw the phasors that represent the following sinusoidal alternating quantities:

a) Two currents with RMS values of 4 amps and 8 amps with the second current leading the first by p/3 radians.

b) Two voltages with RMS values of 10V and 15V with the second voltage leading the first by 36°

5.1 (2)

Z= vXL2+R2

v (8)2+ (15)2

v64+225

v289

Overall impedance=17 ?.

Phase angle=arc tan (XL/R)

Phase angle=arc tan (8/15)

Phase angle=28.0725°

5.1 (3)

5.2 (1)

Series resonance for an RLC circuit

When capacitive reactance, as well as inductive reactance is equal in magnitude but are in phase and apart by 180 degrees, they tend to cancel each other out and the occurrence of resonance in RLC series circuit takes place. For the use in tuning applications, the sharp minimum in impedance is helpful. The minimum sharpness is characterized by the circuit's Q, and is dependent on the value of R.

The resonance condition is typified by zero phase and minimum impedance and is straightforward, in the case of series resonance.

5.2 (2) A typical Phasor diagram showing V and VR at resonance can be seen below.

5.2(3) It is due to the fact that the circuit undergoes a gain in voltage, although being a passive circuit, there is no power gain. Thus, due to this multiplication of voltage, the circuit is used as impedance transformer. The mathematical representation of voltage across inductor is given by,

While the equation for voltage across the capacitor is given by,

5.3

Due to capacitance and inductive reactance being equal in magnitude, 1/?C=?L, then:

Or 2pf =1/vLC,

This can also be expressed as,

fo=1/2p vLC, (since ? = 2pf)

Where fo has the unit hertz, and is the resonance frequency. C is expressed in farads and is capacitance, while L is expressed in henries and is inductance, according to SI units.

5.4

Q factor-definition

A circuit is said to have a greater selectivity if the circuit response is peaked more narrowly around the frequency chosen. If a circuit is more narrowly selective, then it is said to have high Q factor, which is a measure or degree of selectivity. If a circuit is more narrowly selective, then it is said to have high Q factor, which is a measure or degree of selectivity. For a tuned radio frequency receiver and for an RLC circuit in an ideal situation, the Q factor may be mathematically For a tuned radio frequency receiver and for an RLC circuit in an ideal situation, the Q factor may be mathematically represented as,

Where L, R and C are the inductance, resistance and capacitance of the tuned circuit. Moreover, series resistance is inversely proportional to the circuit Q.

Assessment Criteria 6

6.1 (1) Draw the Phasor Diagram for a two branch parallel circuit with C in one branch and L + R in the other branch.

6.2(1) Solution

Z=RXL/vR2+XL2

Phase angle=tan-1 (R/XL)

XL=wL

W=2pf

Therefore, XL=781.65

Z=10*781.65/v100+610987.6

Z=9.999

Phase angle=36.24 degrees.

6.2 (2)V= 100v

I=2A

Theta= 30 degrees.

Z= RXc / vXc^2 + R^2

Xc= 1/ 2 pi f c

3. A circuit consists of a resistance of 60? in parallel with an 8µF capacitor and a supply of ...