6. You are given wires, each with resistance . What is the ratio of maximum to minimum resistance that can be obtained?

To solve this problem, we need to understand how the resistance behaves when wires are combined in series or parallel.

Maximum Resistance:

When resistances are combined in series, the total resistance is the sum of the individual resistances. For n wires, each with resistance , the total resistance in series is:

Rtotal series=nR

So, the maximum possible resistance is nR.

Minimum Resistance:

When resistances are combined in parallel, the total resistance Rtotal parallel is given by the formula:

1/Rtotal parallel=1/R+1/R+⋯ (n terms)

For resistances in parallel, this simplifies to:

1/Rtotal parallel=n/R

Thus, the total resistance in parallel is:

Rtotal parallel=R/n

So, the minimum possible resistance is R/n.

Ratio of Maximum to Minimum Resistance:

The ratio of maximum resistance to minimum resistance is:

Ratio=Maximum Resistance/Minimum Resistance=nR/R/n=n2

Thus, the ratio of the maximum to minimum resistance is n2.

Related Questions:

  1. Can current flow through a circuit without potential difference? Explain.
  2. Can current flow through a circuit without potential difference? Explain.
  3. If aluminum and copper wires of the same length have the same resistance, which has the larger diameter? Why?
  4. What is the resistance across an open switch and a closed switch of a circuit?
  5. Why is a bird sitting on a high-voltage transmission line not electrocuted? Why does it get electrocuted when it touches another wire?
  6. 5. How can you arrange five resistances to form a circuit with resistance smaller than any given resistance?
  7. Physics 10 MCQ
  8. Simple harmonic motion and waves
  9. Simple harmonic motion and waves-NFE
  10. Give an example of vibratory motion which is not simple harmonic motion. Give a reason for your selection.
  11. At the extreme position, velocity is zero but acceleration is maximum in simple harmonic motion. How can you theoretically explain it?
  12. What will happen to the acceleration of a mass-spring system if its mass is doubled?
  13. A simple pendulum has a time period “T”. What will happen to its time period if its thread length is shortened to half?
  14. A simple pendulum has a time period of 4 seconds. Will its time period remain the same or change if its steel bob is replaced by a wooden bob of the same size?
  15. Same masses are attached to different springs, one is vibrating faster. Why?
  16. A simple pendulum has a time period “T” in Murree. In Karachi, it has a different time period. What would you do to make its time period the same as it was in Murree?
  17. What will happen to the frequency of waves in a ripple tank if the time period of the electrical vibrator is decreased? What will happen to the wave speed?
  18. Why do water waves refract at the boundary of shallow water and deep water in a ripple tank experiment?
  19. Under what conditions are waves diffracted the most?
  20. What do you mean by oscillation? Define simple harmonic motion. What are the conditions for a body to perform SHM? Give examples of bodies that perform SHM.