Electronics - Ohm's Law - Discussion

Explanation please.

The power handling capabilities are related by the relation P = I2R. So how the answer is false?

Power = v^2/R so the answer is false.

P = I2R.

And P=V2/R.

i.e power is either proportional to resistance or inversely proportional to R.

So answer may be true or false.

Power is independent to the resistance value.

The answer is false.

If assuming the voltage source to be a constant value. Here is an example why:

Suppose we have a simple series circuit with V = 50 V & R = 10k ohms,
Voltage rating using P= V^2/R =50^2/10k = 0.25 W,
Using P=I^2*R we need to get the value of current first, I =V/R=50/10k 5mA, then P =(5mA)^2(10k) = 0.25W,

But what if we increase the value of resistance, say we make it as 20k ohms with the same value of voltage.

P =V^2/R = 50^2/20k = 0.125W, Using P=I^2*R we again need to solve for the current first,
I = V/R = 50/20k.
I = 2.5mA (CURRENT DECREASES), then P=(2.5mA)^2(20k)=0.125W the power still decreases, why?

Because as the value of resistance increases with a constant voltage source the current also decreases thus, the formulas P=V^2/R and I^2*R will always give the same answer. So for P=V^2/R if R increases the P decreases, for P=I^2*R if R increases, the Current would decrease and Power would still decrease as shown in the example above.