Question

A uniform wire of resistance $R$ and length $L$ is cut into four equal parts, each of length $\dfrac{L}{4}$ which are then connected in parallel combination. The effective resistance of the combination will be:
A. $R$
B. $4R$
C. $\dfrac{R}{4}$
D. $\dfrac{R}{{16}}$

Answer 1

Hint:Here we have applied the concepts of resistance in series and parallel. The resistance is the opposition to a current flow in a circuit. It is also known as the voltage to current ratio.

Complete answer:
The series circuit's total resistance is equal to the number of individual resistances. The voltage is proportional to the sum of the voltage drops applied to the series circuit. The voltage drop in a series circuit over the resistor is directly proportional to the resistor's size. The output current of the first resistor passes through the input of the second resistor in a series circuit, so the current of each resistor is the same.

In a parallel circuit, the entirety of the resistor leads on one side of the resistors is associated together and all the leads on the opposite side are associated together. In a parallel circuit, the net resistance diminishes as more segments are included, on the grounds that there are more ways for the current to go through. The two resistors have a potential difference between them that is identical. In the circuit, the cumulative current is the entire flow through each branch.

A network's equal resistance is the one resistor that might replace the whole network in this manner. A way in which for a given applied voltage we get the same current as we did with a network. Since resistance is directly proportional to length, each part's resistance is $\dfrac{R}{4}$, and then the resistance further becomes one-fourth as they are all connected in parallel. The current resistance then is $\dfrac{R}{{16}}$.

Hence, option D is correct.

Note:Here we have to see whether the resistances are connected in series or parallel. If we add the resistances in series then the answer would be wrong.In an electric circuit, the different components are connected either in series or in parallel to produce different resistive networks. Sometimes, in the same circuit, resistors can be connected in both parallel and series, across different loops to produce a more complex resistive network. These circuits are known as mixed resistor circuits. In the end, however, the total resistance should be known. It is important to know how to do this because resistors never exist in isolation.