Question

The potential drop across 4V battery in the following circuit will be:

Answer 1

Hint: Grouping of cell in series:
When two or more cells are connected one after another then the resulting connection is called a series combination of the cells. In series combination the combination of cells can be replaced with a single is called equivalent cell. We have two ways to connect cells in series (a) Supporting mode and (b) Opposite mode. In supporting mode cells are connected one after another with their opposite polarity while in opposing mode cells are connected one after another with the same polarity.


Complete step by step answer:
To get the required potential drop across 4V cells first of all we have to calculate current in the circuit.

Since 1Ω, 2Ω, and 3Ω resistances are in series. So equivalent resistance in the circuit is given by:-
\[{R_{eq}} = 1\Omega + 2\Omega + 3\Omega \]
\[\therefore {R_{eq}} = 6\Omega \]
As 10V and 4V cells are in opposite modes. So, their equivalent EMF will be given by:-
\[{E_{eq}} = 10V - 4V\]
\[\therefore {E_{eq}} = 6V\]

Applying Ohm's law:-
\[I = \dfrac{{{E_{eq}}}}{{{\operatorname{R} _{eq}}}} = \dfrac{{6V}}{{6\Omega }}\]
\[\therefore I = 1A\]
Now calculating voltage across 4V cell is:
As the current is flowing from positive terminal to negative terminal of the 4V cell, there must be a drop of electric potential across the 4V cell which will be exactly equal to 4V, because the given cell has no internal resistance (ideal cell).

Note: In many complex electrical circuits having two or more than two cells, can be made simpler one by assuming cells as wire if their internal resistance is zero. This trick is quite useful while calculating equivalent resistance and reduces calculation mistakes.