
Derive the expression for power in an electrical circuit.
Answer
499.5k+ views
Hint
According to Ohm's law at a constant temperature, the current flowing through a conductor will be directly proportional to the potential difference between the ends of the conductor. It is also inversely proportional to the resistance offered by the conductor. We can define the electrical power in a circuit as the amount of energy produced or absorbed in a circuit.
Ohm’s law gives that,
(Where, stands for the current in a circuit, stands for the potential difference across the conductor, stands for the resistance offered by the conductor)
(Where, stands for the power, stands for the work done and, stands for the time.)
Complete step by step answer
From Ohm’s law, we know that
The definition of power says that it is the amount of electrical energy produced or consumed by a circuit. Also in other words we can say that the power in a circuit is the amount of work done by the circuit in unit time. It can be written as,
… equation(A)
By the definition of potential difference we know that potential difference is the work done in bringing a charge from infinity to a particular point, we can write it as
(Where stands for the potential difference, stands for the work done and stands for the total charge)
From the above equation, we get
Substituting this expression of in equation (A), we get
… equation(B)
Now, we know that by definition the current is defined as the charge flowing through a conductor per unit of time. That can be written as,
Substituting this value of current in equation (B), we get
Note
Power is measured using the unit watt. In most electrical devices we can see power ratings. Power rating will be given in the units of watts. It indicates the maximum amount of electrical energy converted into any other form of energy by the device. Some electrical devices such as electrical motors denote power in the units of horsepower.
According to Ohm's law at a constant temperature, the current flowing through a conductor will be directly proportional to the potential difference between the ends of the conductor. It is also inversely proportional to the resistance offered by the conductor. We can define the electrical power in a circuit as the amount of energy produced or absorbed in a circuit.
Ohm’s law gives that,
Complete step by step answer
From Ohm’s law, we know that
The definition of power says that it is the amount of electrical energy produced or consumed by a circuit. Also in other words we can say that the power in a circuit is the amount of work done by the circuit in unit time. It can be written as,
By the definition of potential difference we know that potential difference is the work done in bringing a charge from infinity to a particular point, we can write it as
From the above equation, we get
Substituting this expression of
Now, we know that by definition the current is defined as the charge flowing through a conductor per unit of time. That can be written as,
Substituting this value of current in equation (B), we get
Note
Power is measured using the unit watt. In most electrical devices we can see power ratings. Power rating will be given in the units of watts. It indicates the maximum amount of electrical energy converted into any other form of energy by the device. Some electrical devices such as electrical motors denote power in the units of horsepower.
Recently Updated Pages
Master Class 12 Business Studies: Engaging Questions & Answers for Success

Master Class 12 English: Engaging Questions & Answers for Success

Master Class 12 Economics: Engaging Questions & Answers for Success

Master Class 12 Social Science: Engaging Questions & Answers for Success

Master Class 12 Maths: Engaging Questions & Answers for Success

Master Class 12 Chemistry: Engaging Questions & Answers for Success

Trending doubts
Which one of the following is a true fish A Jellyfish class 12 biology CBSE

Which are the Top 10 Largest Countries of the World?

Why is insulin not administered orally to a diabetic class 12 biology CBSE

a Tabulate the differences in the characteristics of class 12 chemistry CBSE

Why is the cell called the structural and functional class 12 biology CBSE

The total number of isomers considering both the structural class 12 chemistry CBSE
