In the circuits shown, the batteries are identical and all have negligible internal resistance. All of the resistors have the same resistance.

Question 20

In the circuits shown, the batteries are identical and all have negligible internal resistance. All of the resistors have the same resistance. The diodes have zero resistance when conducting and infinite resistance when not conducting.

In which circuit is the current in the battery greatest?

 

Reference: Past Exam Paper – June 2018 Paper 12 Q36

Solution:

Answer: A.

Ohm’s law: V = IR

Current I = V / R

For the current to be greatest, the value of resistance R should be smallest.

Connecting resistors in series causes the overall resistance to be greater than the individual resistors, and when resistors are connected in parallel, the overall resistance is smaller than the individual ones.

In this question, we want the overall resistance to be small, so they should be connected in parallel. [B incorrect]

Current flows from the positive terminal to the battery to the negative terminal. A diode would allow current to flow when it is connected in the forward direction (same direction as current). In this question (considering A, C and D), the forward direction of the diode is when it is pointed downwards.

So, any diode pointing upwards in the diagrams (for A, C and D) are connected in the reversed direction. These will not allow current to flow (as in C and D) and so, the resistors in that branch will be short circuited – they will not be considered in the overall resistance.

In other words, the circuits in C and D may be considered to consist of only one resistor as the other one is short circuited and does not contribute any resistance. [C and D are incorrect]

 
Thus, the overall resistance in circuit A is smallest and the current is greatest.