Question

Three $2\Omega$ resistors, A, B, and C are connected as shown in the figure. Each of them dissipates energy and can withstand a maximum power of $18W$ without melting. Find the maximum current that can flow through the three resistors?

Answer 1

Step 1: Given data

Resistances, $R_1=R_2=R_3=2\Omega$

Maximum power, $P=18W$

Step 2: Calculating current through A

Power is calculated by the formula, $P=I^{2}R$

Therefore, the current is given by, $I=\sqrt{\frac{P}{R}}$

Current through the circuit = current through A = $I=\sqrt{\frac{18}{2}}=3A$.

Step 3: Calculating current through B and C

Since resistors B and C are of the same magnitude and are connected in parallel, half of the total current passes through each of them

That is current through B = current through C = $\frac{1}{2}\times 3=1.5A$.

Hence, the maximum current flowing through A is $3A$, and the maximum current flowing through B and C is $1.5A$