Question

In the following circuit, the 10$\Omega$ resistor dissipates power P. If the resistor is replaced by 90$\Omega$, the power dissipated in it is

• A. P
• B. 3P
• C. 9P
• D. P/3

Answer 1

The correct option is A P

Answer is A.
Energy ($power\times time$) is measured in Joules and by including time (t) in the power formulae, the energy dissipated by a component or circuit can be calculated.
Energy dissipated = Pt or $VI\times tasP=VI$.
It can also be written as $I^2\times RtasV=IR.$
Hence, the expression for Power in terms of current is given as $P=I^{2}RtJ$.
When we exclude the time factor, we have, $P=I^{2}RJ$.
Power P when resistance is 1 ohm:
$P={\left(\frac{10}{4}\right)}^2\times 1=\frac{100}{16}$
Power P when resistance is 9 ohm:
$P={\left(\frac{10}{12}\right)}^2\times 9=\frac{100}{12\times 12}\times 9=\frac{100}{16}=P$
Hence, the power dissipated remains the same as P in both cases.