Question

In the circuit diagram shown, what is the maximum number of switches that must be closed to turn on the lights?

A. 3
B. 6
C. 4
D. 5

Answer 1

Hint: To solve this question we need to understand that light bulbs glow when they are in a closed circuit where one side of the bulb is connected to the positive terminal and the other to the negative terminal. For bulbs connected in parallel connection, one side of all bulbs should be connected to one terminal and the other side of bulbs to be connected to another terminal.

Complete step by step solution:
Step 1:
Let us label the components as Bulb 1, Bulb 2, Bulb 3, Bulb 4, Switch 1, Switch 2, Switch 3, Switch 4, Switch 5 and Switch 6.
Step 2:
For a bulb to glow, both of the ends should be connected. So, for Bulb 2, Bulb 3 and Bulb 4 to glow we need to close switch 3, switch 4 and Switch 5.
If we close Switch 1, then both sides of the Bulb 1 will be connected to the same terminal and this leads to a short circuit situation and no current flows through Bulb 1 and it does not glow.
Coming to Switch 6, if we open this switch then the circuit will be open and no bulb will glow as this is the only switch which connects another terminal of the cell to the circuit.
If we close Switch 5, then Bulb 2, Bulb 3 and Bulb 4 will be connected to the same terminal and no current flows through these bulbs. This is called a short circuit situation for these bulbs and these bulbs will not glow. So, Switch 5 should be open.
Step 3:
By creating the below diagram we can easily see how things look.

Step 4:
So, switches which are open are Switch 1 and Switch 5.
So, switches which are closed are Switch 2, Switch 3, Switch 4 and Switch 6.
Therefore, the total number of switches which are open are 4.
So, the correct option is C.

Note:
Short circuit is the situation where no current flows through the object. We should always take care of this situation which may lead to other issues while solving these problems. Switch 6 is one of the important switches here which determines the whole flow of current through the circuit.