Question

The potential difference ${V_A} - {V_B}$ between the point A and B in the given figure is

(A) $ + 9V$
(B) $ - 3V$
(C) $ + 3V$
(D) $ + 6V$

Answer 1

Hint In this question, we can apply Kirchhoff voltage law which implies that the current in a closed loop is zero and the direction of current can be used to see the polarity. Current flows from high potential to low potential.
Formula Used
$V = iR$

Complete step by step answer
 We know that the potential drop across a resistor is the product of the current flowing in it and the resistance.
We consider the sign according to the direction of flow of current that will enter at the positive terminal and leave at the negative one.
Now applying KVL to the given diagram we get,
  {V_A} - (2)(2) - 3 - (2)(1) = {V_B} \Rightarrow {V_A} - {V_B} = 9V \\
    \\

Hence, the correct option is A.

Additional information
Electromotive force or E.M.F of a battery can be defined as the work done in flowing a unit charge from lower potential to higher potential terminal. In an ideal cell, there is no heating observed while in a non-ideal cell there is heating due to internal resistance present. A battery can be used in a circuit in two ways it can act as a source or a load. When a battery is connected in an open circuit means that the current is zero, resistance becomes infinite and the terminal voltage difference seen in the circuit is equal to the emf of the battery. If we take a wire of zero resistance, then the potential at all points will be the same. When two points in a circuit are connected by a conducting wire then we observe the case of short circuiting. In this case the current will be maximum.

Note
 Kirchhoff’s voltage law states that the sum of all potential differences in a closed loop is equal to zero. This implies that Kirchhoff’s law is actually conservation of energy in different words. Law of conservation of energy states that energy can neither be created nor destroyed but only can be transferred from one form to the other form.