9702/Oct Nov/13/2013/Q38

A 20 V d.c. supply is connected to a circuit consisting of five resistors L, M, N, P and Q.

There is a potential drop of 7 V across L and a further 4 V potential drop across N.

What are the potential drops across M, P and Q?

Solution:

Answer: C

This question can be easily tackled by considering the different loops present in the circuit and apply Kirchhoff’s laws to them.

Consider the loop: ‘+’ terminal supply – resistor L – resistor M – ‘-’ terminal supply

From Kirchhoff’s law, the sum of p.d. across any loop should be equal to the e.m.f. Analysis of the loop shows that a 7 V drop across resistor L must mean a 13V drop across M (to obtain a total 20V across L and M).

Notice that the direction of potential drop is also of significance.

Consider resistor L for example. The direction of potential drop is from left to right. Current flows from the ‘+’ terminal of the supply, so the junction on the left of resistor L should be at a higher potential (which is equal to 20V since there is no component between it and the ‘+’ terminal of the supply).

So, the direction of potential rise is from a greater value of potential to a small value of potential. Additionally, current flows from a greater potential to a smaller potential (as in the case of the ‘+’ terminal of the supply).

The junction between L and M is at a potential of 13V (since the right junction to which M is connected is at 0V as it is connected to the ‘-’ terminal of the supply).

There is a potential drop of 4V downwards across N, so current flows downwards. This means that the potential at the upper junction (between L and M) is greater than the lower junction (between P and Q) and the difference in potential is 4V.

Thus, lower junction (between P and Q) is at a potential of (13V – 4V =) 9V

So, the potential drop across resistor Q is 9V (since the right junction to which Q is connected is at 0V as it is connected to the ‘-’ terminal of the supply).

Finally, consider resistor P. Its terminal is at a potential of 20V and its right terminal is at a potential of 9V. Potential drop = 20 – 9 = 11V.

Important notice:

When considering a loop, it should start from one terminal of the supply and end at the other terminal. Only then will Kirchhoff’s law apply. For example, ‘+’ terminal supply – L – N – P – ‘+’ terminal supply is not a correct loop. You may notice that the sum of p.d. is not equal to the e.m.f. Additionally the flow of current is wrong.

Reference: PYQ - Oct/Nov 2013 Paper 13 Q38