You are given a number of 22 Ω resistors, each capable of dissipating only 2.1 W without being destroyed.

Question

You are given a number of 22 Ω resistors, each capable of dissipating only 2.1 W without being destroyed. What is the minimum number of such resistors that you need to combine in series or in parallel to make a 22 Ω resistance that is capable of dissipating at least 8.3 W?

Answer 1

The answer is 4 resistors. These are two parallel combinations of 22 ohm resistors in series.

Each parallel combination consists of two resistors which gives an equivalent resistance of 11 ohms. Two of these in series will give a total equivalent resistance of 22 ohms.

The total current in the circuit can be obtained from P = I²R or I = √P/R = √8.3 / 22 = 0.61 amps.

This current will be divided equally between two parallel resistors to give a current of 0.31 amps in each 22 ohm resistor in parallel. The power dissipated in each resistor is P = 0.31² x 22 = 2.1 watts which meets the criteria for each 22 ohm resistor.

I wish I could have drawn this.