Question

For the following circuit, what is the value of total resistance between X and Y?

Answer 1

Hint: The above problem can be resolved by analysing the circuit diagram and the direction of the current flow. The current will flow from the X-terminal resistance, and then it will directly pass through the Y-terminal. Therefore, we can apply the mathematical relation for the total resistance in a series connection, as the resistors connected in series. Moreover, the concept of Ohm's law can also be used to solve the problem.



Complete step by step solution
We know that the current always passes through the wire that consists of the least magnitude of the resistance because there is the inverse relation between the current and the resistance.
After passing through the first resistance along the X- terminals, the current goes to the first resistor along the Y-terminal. Rather there will be no flow of current through the remaining resistors due to open connection at the other end.
So, the two resistors act as the series connection of the resistances and the total resistance along the terminal X and y is given as,
\[\begin{array}{l}
{R_{total}} = R + R\\
{R_{total}} = 2R
\end{array}\]
Therefore, the value of total resistance between X and Y is 2R.


Note: Try to understand the relationship between the voltage, current, and resistance, collectively known as Ohm's law. Besides, the mathematical relation for the total resistances in the series connection and the parallel connection is also remembered with the firm analysis with the direction of current flow.