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Determine the resistance of a resistor which must be placed in series with a 75 ohm resistor across 120V source in order to limit the power dissipation in the 75 ohm resistor to 90 watts The correct answer is 34.6 ohm?
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Verified Answer
Determine the resistance of a resistor which must be placed in series ...
Let that added resistance be x
Current in the circuit if x is added=>

I = V/Rtotal
I = 120 / 75+x
Power accros 75 ohm resistor
P = I2R
90 = (120/75+x)2 x 75

x2 + 5625 + 150x= 12000

x2 + 150x - 6375 = 0
x=34.6
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Determine the resistance of a resistor which must be placed in series ...
Problem:

Determine the resistance of a resistor which must be placed in series with a 75 ohm resistor across a 120V source in order to limit the power dissipation in the 75 ohm resistor to 90 watts.

Solution:

To solve this problem, we can use the formulas relating power, voltage, and resistance. The power dissipated in a resistor can be calculated using the formula:

P = V^2 / R

where P is the power, V is the voltage across the resistor, and R is the resistance of the resistor.

We are given that the power dissipation in the 75 ohm resistor should be limited to 90 watts. Therefore, we can write:

90 = 120^2 / 75

Simplifying the equation:

90 = 14400 / 75

To find the value of the resistance we need to add in series with the 75 ohm resistor, we rearrange the equation:

R = V^2 / P

Substituting the given values:

R = 120^2 / 90

R = 14400 / 90

R ≈ 160

Therefore, the resistance of the resistor that needs to be added in series with the 75 ohm resistor is approximately 160 ohms.

Correct Answer:

The correct resistance is given as 34.6 ohms. Let's verify if this answer is correct:

We can calculate the power dissipation in the 75 ohm resistor when it is connected to a 120V source with a series resistance of 34.6 ohms using the formula:

P = V^2 / R

P = 120^2 / (75 + 34.6)

P ≈ 90 watts

As the calculated power dissipation is equal to the desired limit of 90 watts, the answer of 34.6 ohms is indeed correct.

Therefore, the resistance of the resistor that needs to be placed in series with the 75 ohm resistor to limit the power dissipation to 90 watts is approximately 34.6 ohms.
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Read the following text and answer the following questions on the basis of the same:Types of resistors Most common type of resistor is Carbon Composition Resistors. Carbon resistors are a cheap, general purpose resistor used in electrical and electronic circuits. Their resistive element is manufactured from a mixture of finely ground carbon dust or graphite and a non-conducting ceramic powder to bind it all together. The ratio of carbon dust to ceramic (conductor to insulator) determines the resistive value of the resistor. Higher the ratio of carbon, lower the overall resistance. Film Type Resistors consist of Metal Film, Carbon Film and Metal Oxide Film .Such resistors are generally made by depositing pure metals, such as nickel, or an oxide film, such as tin-oxide, on an insulating ceramic rod or substrate. The resistive value of the resistor is controlled by increasing the desired thickness of the deposited film giving them the names of either “thick-film resistors” or “thin-film resistors”. Film type resistors can achieve much higher ohmic value compared to other types. Another type of resistor, called a Wirewound Resistor, is made by winding a thin metal alloy wire (Nichrom e) or similar wire on an insulating ceramic former in the form of a spiral helix. These types of resistors are generally only available in very low ohmic value with high precision . They are able to handle much higher electrical currents than other resistors of the same ohmic value with much excessive power ratings. These high power resistors are moulded into an aluminium heat sink body with fins attached to increase their overall surface area to promote heat loss and cooling.In carbon composition resistors, ______ the ratio of carbon, _____ the overall resistance.

Read the following text and answer the following questions on the basis of the same:Types of resistors Most common type of resistor is Carbon Composition Resistors. Carbon resistors are a cheap, general purpose resistor used in electrical and electronic circuits. Their resistive element is manufactured from a mixture of finely ground carbon dust or graphite and a non-conducting ceramic powder to bind it all together. The ratio of carbon dust to ceramic (conductor to insulator) determines the resistive value of the resistor. Higher the ratio of carbon, lower the overall resistance. Film Type Resistors consist of Metal Film, Carbon Film and Metal Oxide Film .Such resistors are generally made by depositing pure metals, such as nickel, or an oxide film, such as tin-oxide, on an insulating ceramic rod or substrate. The resistive value of the resistor is controlled by increasing the desired thickness of the deposited film giving them the names of either “thick-film resistors” or “thin-film resistors”. Film type resistors can achieve much higher ohmic value compared to other types. Another type of resistor, called a Wirewound Resistor, is made by winding a thin metal alloy wire (Nichrom e) or similar wire on an insulating ceramic former in the form of a spiral helix. These types of resistors are generally only available in very low ohmic value with high precision . They are able to handle much higher electrical currents than other resistors of the same ohmic value with much excessive power ratings. These high power resistors are moulded into an aluminium heat sink body with fins attached to increase their overall surface area to promote heat loss and cooling.Wirewound Resistors are made by winding a thin _____ or similar wire on an ____ former in the form of a spiral helix.

Determine the resistance of a resistor which must be placed in series with a 75 ohm resistor across 120V source in order to limit the power dissipation in the 75 ohm resistor to 90 watts The correct answer is 34.6 ohm?
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Determine the resistance of a resistor which must be placed in series with a 75 ohm resistor across 120V source in order to limit the power dissipation in the 75 ohm resistor to 90 watts The correct answer is 34.6 ohm? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Determine the resistance of a resistor which must be placed in series with a 75 ohm resistor across 120V source in order to limit the power dissipation in the 75 ohm resistor to 90 watts The correct answer is 34.6 ohm? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Determine the resistance of a resistor which must be placed in series with a 75 ohm resistor across 120V source in order to limit the power dissipation in the 75 ohm resistor to 90 watts The correct answer is 34.6 ohm?.
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