(a) You need a 45 Ohm resistor, but the stockroom has only 20 Ohm and 50 Ohm res

Question

(a) You need a 45 Ohm resistor, but the stockroom has only 20 Ohm and 50 Ohm resistors. How can the desired resistance be achieved under these circumstances? Put one 50 and one 20 Ohm resistor in series and then put that combination in parallel with a 20 Ohm resistor. Put two 50 Ohm resistors in series and then put that combination in parallel with a 20 Ohm resistor. Put two 50 Ohm resistors in parallel and then put that combination in series with a 20 Ohm resistor. Put one 50 and one 20 Ohm resistor in parallel and then put that combination in series with a 20 Ohm resistor. (b) What can you do if you need a 35 Ohm resistor? Put one 50 and one 20 Ohm resistor in series and two 20 Ohm resistors in series. Then put these two combinations in parallel. Put two 50 Ohm resistors in series and two 20 Ohm resistors in series. Then put these two combinations in parallel. Put one 50 and one 20 Ohm resistor in parallel and two 20 Ohm resistors in parallel. Then put these two combinations in series. Put two 50 Ohm resistors in parallel and two 20 Ohm resistors in parallel. Then put these two combinations in series.

Explanation / Answer

(a)

As we know that

If we put two 50 ohm resistors in parallel the we have equivalent resistance

Equivalent = 1/(1/50 + 1/50)

Equivalent = 25 ohm

Then

put this equivalent with 20 ohm series

So,

Resultant resistance = 25 + 20 = 45 ohm here we have the desired resistance

(b)

If we put Two 50 ohm resistor in parallel so its equivalent

Equivalent50 = 1/(1/50 + 1/50)

Equivalent50 = 25 ohm

If we put Two 20 ohm resistor in parallel so its equivalent

Equivalent20 = 1/(1/20 + 1/20)

Equivalent20 = 10 ohm

Then the final resistance will be = 25 + 10 ohm = 35 ohm

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