Question

What possible values of resultant resistance one can get by combining two resistances, one of value $2\,\Omega$ and the other $6\,\Omega$ ?

Answer 1

In order to answer this question, we will discuss the two possible cases of resultant resistance, and then we will also show the both possible cases numerically.And we will also discuss the cases theoretically.

Complete step by step answer:
There are possible two ways or values of resultant resistance such that-
(i) If the resistors are connected in series, then:
When the same amount of current passes through the resistors, the circuit is said to be linked in series. The voltage across each resistor in such circuits varies. If any resistor in a series connection is broken or a fault occurs, the entire circuit is shut off.
The total resistance $= 2\Omega + 6\Omega = 8\Omega$

(ii) If the resistors are connected in parallel, then:
The potential difference across each resistor is equal to the potential difference across the parallel combination when resistors are linked in parallel. The sum of the currents flowing through each resistor in a parallel combination equals the total current flowing through the combination. A low-resistance conductor carries a significant amount of current.
The total resistance $= \dfrac{1}{2} + \dfrac{1}{6} = \dfrac{4}{6} = \dfrac{2}{3}$

Note: The flow of electric current in a circuit is controlled by resistors. When the same amount of current passes through the resistors, the circuit is said to be linked in series. When the voltage across the resistors is the same, the circuit is said to be linked in parallel.