# Are $\frac{1}{4}$watt 4x$\Omega$ Resistor and $\frac{1}{2}$watt x$\Omega$ Resistor equivalent?

We know Ohm`s law: $$\Omega = \frac{V}{I}$$ $$W=\frac{A}{t} \space\space\space\space\space\space V = \frac{A}{q} \space\space\space\space\space\space I = \frac{q}{t} \space\space\space =>\space\space\space W= VI$$ $$\Omega = \frac{W}{I^2}=\frac{V^2}{W} \space\space\space\space\space\space Right!$$

Lets say I have a $\frac{1}{2}$watt x $\Omega$ resistor in a main circuit,
I need to know can I replace the soldered $\frac{1}{2}$watt x $\Omega$ resistor using another two $\frac{1}{4}$watt 2x $\Omega$ resistors in parallel or using single $\frac{1}{4}$watt 4x $\Omega$ resistor?

I think that if the power supply gives the same voltage before and after replacement across the resistor, then it will flow half current through new resistor and wattage requirement might be satisfied.
I mean if before replacement everything was working correctly and the original resistor was not burned, then the new $\frac{1}{4}$watt 4x $\Omega$ resistor also might work just fine!

Am I right? Is it possible to do? will any problem about voltage drop?
Is it possible to replace Anytime?

• I am confused by your question vs the answer you have accepted. Are you asking about replacing a single 1/2W resistor with two 1/4W resistors, or are you asking about replacing a single 1/2W resistor with a single 1/4W resistor of twice the resistance? – Tut Mar 4 '15 at 12:50
• I was asking to replace 1/2w resistor with two 1/4watt resistor! – IremadzeArchil19910311 Mar 4 '15 at 12:54
• Ok, but now with your edit you have also asked about 1/4W resistor of 4x resistance which is entirely different. Note there is usually a reason in a circuit to use a specific resistance. To substitute with a resistance of 4x is usually a bad idea. – Tut Mar 4 '15 at 12:59
• You right. Thank you! I Edit my mistake! So you mean that it is possible to replace 1/2 watt x ohm single resistor using two 1/4 watt 2x ohm resistor, but can I replace it using single 1/4watt 4x ohm resistor!? – IremadzeArchil19910311 Mar 4 '15 at 13:02
• The answers below are correct regarding two 1/4W resistors. Do not replace with a single 1/4W 4x ohm resistor. That will usually affect the functionality of the circuit and could still burn up as Andy pointed out. – Tut Mar 4 '15 at 13:17

Resistors in parallel dissipate proportional amounts of the total power from each depending on the proportion of the current that is flowing through them.

Two equal resistors in parallel will share the current equally. Ergo, they will dissipate half the total power each.

So yes, two equal resistors of twice the value and half the power in parallel will handle the same power as the original resistor.

To reiterate the maths differently:

Original = 1W, 50Ω. Current would be $\sqrt{1/50}$ = 0.141A.

100Ω resistor with half the current flowing would be $(0.141/2)^2) \times 100$ = 0.5W.

• Thank you! I made mistake: you are right! 1/4 watt x ohm resistor is equivalent to two 1/2 watt 2x ohm resistor is parallel! – IremadzeArchil19910311 Mar 4 '15 at 12:48

I'm having a hard time understanding your notation. R is usually resistance. Stick to that.

R = V/I

Anyways, if you have a 0.5W resistor then the equivalent of that same resistor is two 0.25W resistors in parallel. However, because the resistance is in parallel, that means you need to increase the value of each resistor to compensate.

For example

500 ohm @ 0.5W would be equivalent to two 1kohm @ 0.25W in in parallel.

• OK. Thank you! Also you are right " R is usually resistance"! – IremadzeArchil19910311 Mar 4 '15 at 12:40

Is it possible to replace Anytime?

No they are not equivalent - the 1/4 watt resistor can dissipate power up to a nominal maximum of 1/4 watt whereas the half watt resistor can dissipate more power without burning out.

If the resistor is just across a fixed voltage then yes you can but, it could be across the output of a constant current circuit in which case the current will remain the same thru either resistor and the quarter watt 2X ohm component will burn off twice as many watts as the half watt 1X ohm resistor.

Without knowing the precise detail of the circuit there are no other generalizations.