A grinder motor is designed to operate at a current of 5 A and at a potential difference. ____Ω resistance must be connected in series with the motor so as to maintain the rated current when it is operated on a line.

A grinder motor is designed to operate at a current of 5 A and at a potential difference. ____$\Omega$ resistance must be connected in series with the motor so as to maintain the rated current when it is operated on a line.

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Solution:

Concept- The resistance that must be connected in series is 4 ohms. We will first calculate the motor's resistance using Ohm's law. Next, we'll apply Ohm's law once more to the second situation by connecting a new resistor in series with the motor. When linked in series, the current flow won't alter. To ascertain the results, we will experiment suitably.
The information below is provided in the question:
The grinder motor's rated current is .
The grinder motor's rated potential difference is .
To keep the motor's rated current while it is run on a battery, we are requested to determine the resistance that must be connected in series with the motor line.
Finding the motor's internal resistance is the first step. The new resistor must then be adjusted when the voltage is increased to . However, in order for the current flow to stay the same in the second scenario, the resistor needs to be connected in series with the motor. As is well known, the current flow is constant in a series connection.
Now, we use Ohm's law to calculate the motor's resistance.
Ohm's law states that:,
Where
V denotes a possible discrepancy.
The current flow is indicated by i.
R denotes the motor's resistance.
By changing the necessary variables in equation (1) , we obtain:
The motor's resistance is calculated to be .
Now, we connect a new resistor r in series with the motor for the second scenario.
Therefore, the new net resistance will be .
When we once more use Ohm's law, we get:
Once more, we simplify:In order to retain the motor's rated current while it is run on a battery, the resistance must be linked in series with the motor line is .
Hence, the correct answer is .

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