A voltage of 200V is applied to a tapped resistor of 500 ohm. Find the resistance between two tapping points connected to a circuit needing 0.1A at 25V. I have solved this problem with two approach. But the correct answer is coming only by one approach. Fig.1

Total resistance is Ra+Rb = 500 ohm.
Va+Vb = 200V ; Vb = 25V ;

Hence Va = 175V.
Applying KCL at the tapping point we get:
-I + 0.1 + 25/Rb = 0 ; I = 0.1 + 25/Rb;
Va = I.Ra;
175 = (0.1 + 25/Rb)(500-Rb)
If we solve we will get Ra = 420.85 ohm and Rb = 79.15 ohm.

So far so good.


Consider second image in which Ra and Rb variable are taken such that Ra + Rb = 500 ohm
Va = 175V
Applying KCL at the tapping point we get:
-I + 0.1 + 25/(500-Ra) = 0 ; I = 0.1 + 25/500-Ra;
Va = I.Ra;
175 = (0.1 + 25/500-Ra)(Ra)
If we solve we will get Ra = 2079.15 ohm.
which is wrong, but I am unable to understand the flaw in the second case. It is perfectly fine. The answer is not correct. Just by changing the way variable are taken the answer is changing.

  • \$\begingroup\$ Shouldn't it be Va = IRa in both cases? \$\endgroup\$ – Transistor Aug 26 '18 at 8:35
  • \$\begingroup\$ Yes, Va = I.Ra ; I have changed. \$\endgroup\$ – TapasX Aug 26 '18 at 8:52
  • \$\begingroup\$ And did you recalculate? Did it solve the problem? \$\endgroup\$ – Transistor Aug 26 '18 at 9:04
  • \$\begingroup\$ There is nothing to recalculate. I had forgotten to put Ra in place of R. Calculations remains same. \$\endgroup\$ – TapasX Aug 26 '18 at 11:10

The flaw is that this equation has some restrictions when applied to a real circuit. From a mathematical perspective the second solution is correct. But as still applied that


you would end up with a negative resistance for

\$Ra = -1579\Omega\$

In the real world such a thing doesn't exist and therefore the solution is not applicable for your problem.

  • \$\begingroup\$ If Rb is less than 500, then Ra will be always positive. \$\endgroup\$ – TapasX Aug 26 '18 at 11:14
  • \$\begingroup\$ I agree yes... but that doesn't change the fact that one of your solutions is resulting in a negative Ra \$\endgroup\$ – Humpawumpa Aug 26 '18 at 15:33

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.