Question

You can given one hundred 1 Ω resistors. What is the smallest and largest resistance you can make in a circuit using these?; You can given one hundred 1 Ω resistors. What is the smallest and largest resistance you can make in a circuit using these?

Answer 1

Answer:

Given:

Hundred 1 ohm resistors have been provided in a circuit.

To create:

A circuit having

• Highest equivalent resistance
• Lowest equivalent resistance

Concept:

In a combination of resistances, we should remember that

• Equivalent resistance in series is greater than individual resistances.
• Equivalent resistance in parallel is lower than the individual resistances.

Calculation:

For max resistance:

Resistances are to be connected in series .

R eq. = 1 + 1 + 1 + ....100 times.

=> R eq. = 100 ohms

For min resistance:

Resistances have to be connected in parallel .

1/R eq. = 1/1 + 1/1 +..... 100 times

=> 1/R eq. = 100

=> R eq. = 1/100

=> R eq. = 0.01 ohms

Answer 2

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Given :

100 resistance each of 1 ohm are given

___________________________

To Find :

Equivalent resistance in series and in parallel.

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Solution :

If 100 ohm resistance are given ,

then we can get minimum value of resistnce only when all the resistances are connected in series .

$\star {\boxed{R_{s} \: = \: R_{1} + R_{2} + ....... + R_{100}}}$

Putting Values

» Max. Resistance = 1 + 1 +........100 times

Maximum Resistance = 100 ohms

___________________________

For getting minimum value of the equivalent we need to connect all the resistance in parallel .

$\star {\boxed{\dfrac{1}{R_{p} }\: = \:\dfrac{1}{ R _{1}} + \dfrac{1}{R_{2}}+ ....... + \dfrac{1}{R_{100}}}}$

Put Values

» 1/Min.Resistance = 1/1 + 1/1.............100 times

We get,

» 1/Min.Resistance = 1/100

» Min.Resistance = 0.01 ohms

So,

Minimum Resistance is 0.01 ohms