Question

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

Answer 1

Hint- Use the formula for power decipated in a resistor in terms of current

Step 1 : Finding maximum current flowing through $A$.

Given: Maximum power each resistor can withstand is $18W$

We know that $P$ = $I^2\times R$

Where $P$ - Power , $I$ - Current , $R$ - Resistance

Putting the value of $P$ and $R$

$18$ = $I^2\times 2$

$I^2$ = $9$

$I$ = $3$

This is maximum value of current passing through $A$.

Step 2 : Finding maximum current flowing through B and C.

As resistance $B$ and $C$ are equal so current $I$ will get equally distributed in $B$ and $C$

So maximum current in $B$ and $C$ is $1.5A$

Final Step-

Maximum current that can flow through $A$ is $3A$

Maximum current that will flow through $B$ and $C$ is $1.5A$