Question

In the circuit shown in Fig. all the resistors are rated at a maximum power of 1.00 W. What is the maximum emf $ϵ$ that the battery can have without burning up any of the resistors?

Answer 1

In the circuit current i flows in the circuit
We know that Power$=i^{2}R$
$\Rightarrow 1=i^{2}R$ (Given $P=1W$)
$i=\frac{1}{\sqrt{R}}$ -> limitting value of current in resistance
As current increases, the resistor which will first burn is having greatest resistance
In the circuit we have $40\Omega$ resistors
if this resistor is safe all other will be safe
Limitting value of current$=i=\frac{1}{\sqrt{40}}=\frac{1}{2\sqrt{10}}A$
So the value of $E=iR$
$=\frac{1}{2\sqrt{10}}\times 126.382$
$=19.982$
$E\approx 20V$