Question

Observe the circuit and answer the questions given below:

(a) Are the resistors 3 and 4 in series?
(b) Are the resistors 1 and 2 in series?
(c) Is the battery in series with any resistor?
(d) What is the potential drop across the resistor 3?
(e) What is the total emf in the circuit if the potential drop across resistor 1 is 6V.

Answer 1

Hint : As a first step, read the question well along with the sub questions given and also analyse the circuit well. Then look for the series and parallel connections and hence answer the first three sub questions. Now accordingly find the potential drop across resistor 3 and also the total emf.

Complete step-by-step solution:
In the question we are given a circuit with a voltage source and 4 resistors and we have 5 sub questions following this. Let us first analyse the circuit and hence answer the question.
In order to make the first and second sub question easy we are given the polarity for the resistors.
(a) For the resistors 3 and 4 you could say that they are connected in series as the connection is made end to end. So, the answer here is ‘yes’.
(b) Yes the resistors 1 and 2 are connected in series.
(C) Yes, Resistors 1 and 2 are connected in series with the battery.
(d) Since the resistors 3 and 4 are in series connection and the combination is in parallel with ${{V}_{2}}$, we could say that,
${{V}_{3}}+{{V}_{4}}={{V}_{2}}$
$\Rightarrow {{V}_{3}}=14-8=6V$
Therefore, potential drop across resistor 3 is 6V.
(e) Total emf of the circuit could be found simply by the sum of resistors 1 and 2. That is,
${{V}_{1}}+{{V}_{2}}=6+14=20V$
Therefore, we found the net emf of the circuit to be 20V.

Note: A circuit is said to be series when the flow of current is found to be the same in all of the components in the circuit and the circuit is parallel when there are two or even more than two paths for current flow. A fault at a single point would cause the breakage of the total circuit.