Test: Dependent & Independent Sources - 1 - Electrical Engineering (EE) MCQ

Norton’s Theorem:

Any two terminal bilateral linear DC circuits can be replaced by an equivalent circuit consisting of a current source and a parallel resistor.

Constant Current Control:

• This method of current control regulates the current by adjusting the duty cycle to maintain a constant output current regardless of changes to the input voltage and output resistance.
• A power supply operating in constant current mode will compare its reference against the scaled output current. This can be accomplished through the use of a hall effect sensor, a shunt with a differential amplifier, or any other current to voltage conversion method. 
• The process of comparing the reference against the scaled output current generates an error signal which is then amplified.

Concept:

Ideal voltage source: An ideal voltage source have zero internal resistance.
Practical voltage source: A practical voltage source consists of an ideal voltage source (V_S) in series with internal resistance (R_S) as follows.
An ideal voltage source and a practical voltage source can be represented as shown in the figure.

Ideal current source: An ideal current source has infinite resistance. Infinite resistance is equivalent to zero conductance. So, an ideal current source has zero conductance.
Practical current source: A practical current source is equivalent to an ideal current source in parallel with high resistance or low conductance.
Ideal and practical current sources are represented as shown in the below figure.

• When an ideal voltage source and an ideal current source in series, the combination has an ideal current sources property.
• Current in the circuit is independent of any element connected in series to it.
   

Explanation:

In a series circuit, the current flows through all the elements is the same. Thus, any element connected in series with an ideal current source is redundant and it is equivalent to an ideal current source only.

In a parallel circuit, the voltage across all the elements is the same. Thus, any element connected in parallel with an ideal voltage source is redundant and it is equivalent to an ideal voltage source only.

Concept:

Ideal Current Source: An ideal current source has infinite resistance. Infinite resistance is equivalent to zero conductance. So, an ideal current source has zero conductance.
Practical Current Source: A practical current source is equivalent to an ideal current source in parallel with high resistance or low conductance.
Ideal and practical current sources are represented as shown in the below figure.

Calculation:

 

Resistive load R_L = 5 × 10³ Ω 
Current through load I_L= 20 × 10^-3 A
Internal resistance = r
Voltage across load, V_L = R_L × I_L
= 5 × 10³ × 20 × 10^-3
= 100 V
The net current through internal resistance
r = 25 mA - 20 mA = 5 mA
Voltage across internal resistance = current × r
100 = 5 × 10^-3 × r
r = 20 kΩ

To neglect a voltage source, the terminal across the sources are short-circuited. Because ideally, the internal resistance of the voltage source is zero.

To neglect a current source, the terminal across the sources are open-circuited. Because ideally, the internal resistance of the current source is infinite.

When batteries are connected in parallel it must be ensured that they have the same emf to avoid short circuits and to avoid any circulating current between batteries..

• In every practical voltage source, there is some electrical resistance inside it. This resistance is called the internal resistance of the source.
• When the terminal of the source is open-circuited, there is no current flowing through it; hence there is no voltage drop inside the source but when the load is connected with the source, current starts flowing through the load as well as the source itself.
• But in an ideal voltage source, this difference is considered as zero that means there would not be any voltage drop in it when current flows through it and this implies that the internal resistance of an ideal source must be zero.

This can be concluded that voltage across the source remains constant for all values of load current.

The V-I characteristics of an ideal voltage source are shown below.

Ideal case with noise effect,
Considering the effect of noise, Ideal Voltage Source delivers constant voltage irrespective of the value of current through it and V-I characteristics are given as:

Ideal Current Source: An ideal current source has infinite resistance. Infinite resistance is equivalent to zero conductance. So, an ideal current source has zero conductance.

Practical Current Source: A practical current source is equivalent to an ideal current source in parallel with a high resistance or low conductance.

Ideal and practical current sources are represented as shown the below figure.

By using the fact that the current is same in series connection resistors and voltage is same parallel, the above problem can be solved. I0 is divided into αIx and Ix. So, calculation these two gives the required current value.

Dependant sources are also known as Controlled sources as there are controlled by other elements present in the circuit.