Why do resistors in parallel not follow the trend?

[markm]

hi. ^_^

we recently did this experiment on measuring the actual resistances of resistors. every time, the actual resistance was less than the resistance on the label, except for the resistors arranged in parallel.

the theoretical value for 100 ohm and 220 ohm resistors is 67.5 ohms, but our reading is 68 ohms.

in the series arrangement the value was supposed to be 320 ohms, but we got just 316 ohms. when we measured individual resistances, the measured value was also always less than the theoretical one.

does anyone know the explanation why the resistors in parallel don't follow the trend? thanks so much..

 

[maverick280857]

Just curious...how are you measuring the "actual" resistance anyway?

 

[markm]

with a multimeter

 

[maverick280857]

Haha okay.

the theoretical value for 100 ohm and 220 ohm resistors is 67.5 ohms, but our reading is 68 ohms.

First off

$$R_{||} = \frac{(220)(100)}{320} = 68.75$$ on windoze calc...

And now it depends on your multimeter's predicted error interval. The 4 ohm difference seems quite large considering the low error in the parallel resistance measurement. Can you see why? (error wise)

Cheers
Vivek

 

[Zaimeen]

the theoretical value for 100 ohm and 220 ohm resistors is 67.5 ohms, but our reading is 68 ohms.

The theoretical value should be 68.75 Ohms ! And that's the "calculated" value. So, your actual value is 68 Ohms, which is consistent with any real value!

You should expect your values to be less than the theoretical values because of various reasons: -

1. Energy loss due to resistance of wires in your apparatus. Wires heat up during the experiment due to there resistances and energy is dissipated form there

2. Internal resistance of your measuring instrument (multimeter)

3. Loose connections while setting up the apparatus. This lead to unaccurate readings obtained.

4. Your real measurement depends on the least count of the multimeter!

...so many reasons...