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Consider a circuit which has constant source of 100V and Power of 50W.The circuit is purely resistive with resistance of 5 ohms,

From Power law $I=P/V$ so $I=50/100 =0.5$A, but from ohm's law $I=V\div R=100/5=20$A. Which one is to be considered correct? Also, if $I=0.5$ we have power dissipated at resistor $I^2 R = 0.5^2\times 5=1.25$W, so what happens to the remaining power ?

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    $\begingroup$ The contradiction lies in your assumptions. If you put 100V across a 5 Ohm resistor, the power dissipated will be $P= V^2/R = 2000$ W. If the power source can only supply 50 W, then it won't be able to sustain a 100 V potential across the resistor terminals. $\endgroup$
    – Jakob KS
    Commented Sep 8 at 10:12
  • $\begingroup$ @JakobKS sounds like an answer, not a comment. $\endgroup$
    – ProfRob
    Commented Sep 8 at 10:24
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    $\begingroup$ A common cause for confusion like this is that many power supplies will list themselves as 50W, when they actually mean they have a maximum output of 50W $\endgroup$
    – Cort Ammon
    Commented Sep 8 at 16:31

2 Answers 2

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Of the 4 variables in your circuit $V$, $I$, $R$, and $P$, only two are independent. That is, if you pick two, say voltage and power, the other two can be calculated from those two.

If you pick that the voltage is 100 V, and the power is 50 W, then the current is necessarily 0.5 A, (50 W / 100 V) and the resistance is therefore necessarily 200 $\Omega$ (100 V / 0.5 A).

If you pick that the voltage is 100 V, and the resistance is 5 $\Omega$, then the current is necessarily 20 A (100 V / 5 $\Omega$), and the power is then necessarily 2000 W (100 V x 20 A).

You cannot pick that the voltage is 100 V, the power 50 W and the resistance 5 $\Omega$, because you have picked three variables, of which only two are independent, and you have picked three values that are not consistent with one another.

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Your error lies in the assumption that the power is 50 w when a 5$\Omega$ resistor is connected to a constant 100 V source.

In the equation $$P=VI$$

$I$ and $V$ are not independent variables since $$V=IR$$ which results in

$$P=\frac{V^{2}}{R}=2000 w$$

Hope this helps.

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