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.

• A. 3 A.
• B. $\sqrt{6}$ A.
• C. $\sqrt{18}$ A
• D. Data insufficient

Answer 1

The correct option is B $\sqrt{6}$ A.

The power in a circuit is given as P=IV. The power in terms of current and resistance can be derived from the above equation as follows.
We know that from Ohm's law, V=IR. Substituting this in the above equation, we have P=I(IR), that is $P=I^{2}R$.
The resistance across B and C is 1 ohm as they are parallelly connected. The total resistance in the circuit is $2+1=3ohms$.
Given that the power is 18 W and the total resistance is 3 ohms, the maximum current across the circuit is calculated as follows.
$P=I^{2}R$ That is, $I=\sqrt{\frac{P}{R}}=\sqrt{\frac{18}{3}}$.