Maximum Power Transfer Theorem Questions

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Very Short Answers Questions [1 Mark Questions]

Ques. If the source impedance is complex, then maximum power transfer occurs when the load impedance is _______ the source impedance.

1. complex conjugate of
2. negative of
3. negative of the complex conjugate of
4. equal to

Ans. The correct answer is a. complex conjugate of

Explanation: Complex impedance circuits can be solved using the maximum power transfer theorem. Maximum power transfer occurs when the load impedance is the complex conjugate of the source impedance when the source impedance is complex.

Ques. The DC voltage source will deliver maximum power to the variable load resistor if the load resistance is

1. Lesser than the source resistance
2. Zero
3. Greater than the source resistance
4. Equal to the source resistance

Ans. The correct answer is d. Equal to the source resistance

Explanation: The maximum power transfer theorem states that the load resistance must be equal to the source resistance in order to supply maximum power.

Ques. Maximum power transfer theorem functions only when there is a

1. Variable load
2. non-variable load
3. No load
4. None of the above

Ans. The correct answer is a. Variable load

Explanation: The maximum power transfer theorem only works with varying loads.

Ques. Can the maximum power transfer theorem be applied to alternating current circuits?

1. Yes
2. No

Ans. The correct answer is a. Yes

Explanation: Alternating current circuits can be solved using the maximum power transfer theorem.

Ques. Power delivered to the load is given by the formula

1. P_L = I² + R_L
2. P_L = I²R_L
3. P_L = I² - R_L
4. P_L = I² + R²_L

Ans. The correct answer is b. P_L = I²R_L

Explanation: If I be the current flowing through a load of resistance RL, then power delivered to the load is given by

P_L = I²R_L

Ques. The maximum power transfer theorem can be applied to nonlinear networks.

1. True
2. False

Ans. The correct answer is b. False

Explanation: For unilateral and nonlinear networks, the maximum power transfer theorem cannot be used.

Ques. The maximum power transfer theorem is given by the formula:

1. P_max = \(\frac{V_{th}^2}{R_{th}}\)
2. P_max = \(\frac{V_{th}^2}{3R_{th}}\)
3. P_max = \(\frac{V_{th}^2}{4R_{th}}\)
4. P_max = \(\frac{V_{th}}{4R_{th}}\)

Ans. The correct answer is d. P_max = \(\frac{V_{th}^2}{4R_{th}}\)

Explanation: The maximum power transfer theorem formula is given by

P_max = \(\frac{V_{th}^2}{4R_{th}}\)

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Short Answers Questions [2 Marks Questions]

Ques. What is the maximum power transfer theorem?

Ans. The maximum power transfer theorem states that when the load resistance equals the source resistance, the voltage source in a DC circuit will supply maximum power to the resistive load connected to the voltage source.

Ques. Give the formula of the maximum power transfer theorem.

Ans. The formula of the maximum power transfer theorem is

(P_L)_max = \(\frac{V_{th}^2}{4R_{th}}\)

Where

• (P_L)_max is the maximum power delivered to the load resistance
• V_th is the Thevenin voltage
• R_th is the Thevenin resistance

Ques. What is the condition for maximum power delivered to load?

Ans. According to the maximum power transfer theorem, when the load resistance becomes equal to the source resistance or Thevenin resistance, then the maximum power is delivered to the load resistance i.e.

R_L = R_Th

Where

• R_L is the load resistance
• R_Th is the Thevenin resistance

Ques. Does maximum power transfer imply maximum efficiency?

Ans. Maximum power transfer does not imply maximum efficiency. If the load resistance is less than the source resistance, the power dissipated at the load decreases while the majority of the power is dissipated at the source, and the efficiency drops.

Ques. On what factors does maximum power transfer depend?

Ans. The maximum power transfer theorem determines the value of resistance RL that will allow the maximum power to be transmitted from the source to the load. Actually, the maximum power taken from the source depends on the load resistance.

Ques. What will be the efficiency when the source delivers maximum power to the load?

Ans. When maximum power transfer is attained, the efficiency is only 50%, but it approaches 100% when the load resistance approaches infinity, even if the overall power level tends to zero.

Ques. Where and why maximum power transfer theorem is applied?

Ans. Maximum power gets delivered to the load when the load impedance equals the Thevenin impedance. The maximum power theorem states that the maximum power transmission to the load occurs when the load resistance equals the source resistance or Thevenin resistance. In electrical circuits, the maximum power transfer theorem is utilized.

Ques. Give an example of a circumstance in which the maximum power transfer theorem is not applicable.

Ans. Maximum power transfer is incompatible with the objective of minimum noise. For example, the low-level radio frequency amplifier between the antenna and a radio receiver is usually constructed to produce as little noise as possible.

Ques. Define Thevenin’s resistance.

Ans. Thevenin's resistance is the equivalent resistance of a linear electrical circuit viewed from two terminals, where all voltage sources are replaced by internal resistances and all current sources are open circuits.

Ques. Define Thevenin’s voltage.

Ans. The open-circuit voltage across the two terminals of a linear electrical circuit is known as Thevenin's voltage. It is the voltage measured across the terminals if no load is connected.

Ques. What is Thevenin’s Theorem?

Ans. According to Thevenin's theorem, any linear circuit, no matter how complicated, may be simplified to an equivalent circuit with a single voltage source and a series resistance.

Also Read:

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Long Answers Questions [3 Marks Questions]

Ques. What are the limitations of the Maximum Power Transfer Theorem?

Ans. The Maximum Power Transfer Theorem states that when the load resistance equals the source resistance, the maximum power is transmitted from a source to a load. However, this theorem has certain limitations. These are

• This theorem cannot be applied to nonlinear and unilateral networks, It can only be applied to linear and bilateral networks.
• Only 50% efficiency is possible. This indicates that half of the power from the source is wasted in the load, while the other half is dissipated in the source. This is not beneficial to power systems, which require high efficiency.
• It does not consider the voltage regulation at the load. Even though the load current changes, it is essential in power systems to maintain a constant voltage at the load.

Ques. What are the steps to solve a network using the maximum power transfer theorem?

Ans. The following are the steps to solve a network using the maximum power transfer theorem

• Step 1: Determine the variable load resistance in the circuit and eliminate it.
• Step 2: Short-circuit the terminals to replace the independent source voltage, then open the terminals to replace the independent current source.
• Step 3: Calculate the equivalent resistance between the terminals of the open-circuited load resistance to get the circuit's Thevenin resistance.
• Step 4: Calculate the voltage across the terminals of the open-circuited load resistance to determine the Thevenin voltage, then use the maximum power transfer theorem formula to determine the maximum power delivered.

Ques. What are the advantages of the maximum power transfer theorem?

Ans. The following are the advantages of the maximum power transfer theorem

• It is simple to use. The only requirement is that the network be both linear and bilateral.
• It can be applied to both AC and DC circuits.
• It can be used to construct circuits with maximum power transfer or efficiency.
• It may be used to determine the performance of existing circuits.

Ques. Explain how the maximum power transfer theorem can be used to design a power amplifier for maximum efficiency.

Ans. According to the maximum power transfer theorem, maximum power can be transferred from a source to a load when the load resistance equals the source resistance. This indicates that when designing a power amplifier for the greatest efficiency, we should select a load resistance equal to the amplifier's output resistance.

The procedure to use the maximum power transfer theorem to construct a power amplifier for maximum efficiency is

• Determine the output resistance of the power amplifier. This may be achieved by measuring the resistance between the amplifier's output terminals while no load is provided.
• Select a load resistance equal to the output resistance of the amplifier.
• Connect the load to the amplifier's output terminals.
• When the load resistance equals the amplifier's output resistance, the amplifier will provide the maximum power to the load. This indicates that the amplifier will operate at maximum efficiency.

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Very Long Answers Questions [5 Marks Questions]

Ques. Prove the maximum power transfer theorem.

Ans. Consider a circuit in which a load resistance RL is connected in series with the Thevenin’s resistance Rth. Let a voltage source known as Thevenin’s voltage is applied across the terminal of the circuit.

According to Ohm’s law, the current flowing through the circuit is given by

\(I = \frac{V_{th}}{R_L+R_{th}}\)

Where

• I is the current flowing through the circuit
• V_th is the Thevenin voltage
• R_L is the load resistance
• R_th is the Thevenin resistance

Power delivered to the load resistance is given by

P_L = I²R_L

On substituting the value of I, the above equation becomes

P_L = \(( \frac{V_{th}}{R_L+R_{th}})^2 R_L\)

Load power can be maximized by adjusting the value of load resistance RL. Hence the condition for the maximum power to be obtained is

\(\frac{dP_L}{dR_L}=0\)

⇒ \(\frac{d}{dR_L} (\frac{V_th}{R_L+R_th})^2R_L = 0\)

⇒ \(\frac{V_{th}^2(R_{th}-R_L)}{(R_{th}+R_L)^2} = 0\)

⇒ R_th – R_L = 0

⇒ R_th = R_L

Hence, when the thevenin resistance equals the load resistance, the power transferred to the load resistance is maximized.

Ques. What are the applications of the maximum power transfer theorem?

Ans. The following are the applications of the maximum power transfer theorem

• The maximum power transfer theorem can be used for linear networks, the network system, and elements such as R, L, C, and restrained linear sources.
• The maximum power transfer theorem can only be applied when there is a variable load. If not, select the lowest possible internal impedance source that allows maximum current through the fixed load. As a result, the load circuit outputs maximum power.
• This technique is a basis for large sound systems. Maximum power transfer is achieved in the circuit by having the resistance of the speaker (load) equal to the resistance of the amplifier. Both the speaker and the amplifier are considered harmonized when their resistances are equivalent.
• Another use is the relationship between an automobile engine's starting motor and battery. The amount of power provided to the starter is determined by the motor's effective resistance and the battery's resistance. When their levels are equal, the most powerful signal is sent to start the engine.

Ques. Obtain the expression for maximum power delivered to the load resistance using the maximum power transfer theorem.

Ans. According to Ohm’s law, the current flowing through the circuit is given by

\(I = \frac{V_{th}}{R_L+R_{th}}\)

Where

• I is the current flowing through the circuit
• V_th is the Thevenin voltage
• R_L is the load resistance
• R_th is the Thevenin resistance

Power delivered to the load resistance is given by

P_L = I²R_L

On substituting the value of I, the above equation becomes

P_L = \(( \frac{V_{th}}{R_L+R_{th}})^2 R_L\)  …(i)

Now according to the maximum power transfer theorem, power delivered to the load resistance will be maximum when the resistance of the load equals the Thevenin resistance i.e.

R_L = R_th

Hence equation (i) becomes

(P_L)_max = \((\frac{V_{th}}{R_{th}+R_{th}})^2R_{th}\)

⇒ (P_L)_max = \((\frac{V_{th}}{2R_{th}})^2R_{th}\)

⇒ (P_L)_max = \(\frac{V_{th}^2}{4R_{th}}^2R_{th}\)

⇒ (P_L)_max = \(\frac{V_{th}^2}{4R_{th}}\)

The above equation is the maximum power transfer formula used for calculating the maximum power transferred to the load. Therefore, knowing the Thevenin voltage and resistance helps us to determine the maximum power provided to load.

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