Question

In the following circuit, the $1\Omega$. resistor dissipates power $P$. If the resistor is replaced by $9\Omega$. The power dissipated in it is:

• A. $P$
• B. $3P$
• C. $9P$
• D. $P/3$

Answer 1

The correct option is A $P$

As we see that in this circuit all the connection are in series,hence when the circuit is in series there will not be any effect on power of circuit by replacing it's resistance.
Mathematically we know that power(P)=$\frac{\stackrel{2}{v}}{R}$.
so power(P)$\propto$=$\stackrel{2}{v}$ and it will not depend on the value of resistance,therefore we can say the power will remain same on replacing1$\Omega$ with 9$\Omega$.
CONCLUSION: Power is a function of voltage only and it will vary square times its voltage and we obtained a parabolic graph between power and voltage.