Question

In a parallel combination of resistances:
A) P.d. is same across each resistance
B) Total resistance is increased
C) Current is the same in each resistance
D) All above are true

Answer 1

Hint: Resistors are said to have a parallel connection when both their terminals will be connected with the respective terminals of other resistors. To make it clearer, let us call one of the two terminals of the resistors in a circuit as A and let the other terminal be B for all the resistors. In a parallel combination the A terminal of all the resistors will be connected with each other, similarly the B terminals are also connected with the B terminals of other resistors.

Complete step by step solution:
In a circuit if the components are connected in parallel, the voltage will be the same across all the components. Because all components are connected to the same voltage source and the sum of total currents through the components are also the same. This means that if the resistors are connected in parallel then all the resistors will have the same voltage across them.
This shows that option A is correct.
Moving on to the second option,
In a parallel combination of resistance the total resistance is given by,
${\dfrac{1}{R}_{total}} = \dfrac{1}{{{R_1}}} + \dfrac{1}{{{R_2}}} + .....\dfrac{1}{{{R_n}}}$
The net resistance will be,
$R = R_{total}^{ - 1}$
This shows that the second option is not true.
The total current flowing through a parallel combination of resistors will be the individual sum of currents of each branch. The need not be necessarily the same. If the resistors in the combination has different values, then the currents will also be different in different branches, because current will depend on the value of resistance.
The third option is also false.

Therefore the answer is: Option (A), P.d. is the same across each resistance.

Note: In parallel combination the equivalent resistance of the circuit will be lower than the value of the smallest resistor in the circuit. At the same time, in a series combination the value of total resistance will be greater than the value of the highest resistor of the circuit. The current flowing through each resistor in a parallel combination can be obtained by using Ohm’s law.