Q|C (a) You need a 45-ω resistor, but the stockroom has only 20-ω and 50-ω resistors. How can the desired resistance be achieved

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alisha [4.7K]

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Q|C (a) You need a 45-ω resistor, but the stockroom has only 20-ω and 50-ω resistors. How can the desired resistance be achieved

under these circumstances?

Physics

1 answer:

NNADVOKAT [17] · Answer 1 · 2023-08-10T17:16:29+03:00

In order to achieve the desired resistance under the given circumstances, we would connect two 50 Ohms resistors in parallel and then connect it in series with the 20 Ohms resistors.
In order to get a 35 Ohms resistance under the given circumstances, we would connect two 50 Ohms resistors in parallel and then connect it in series with two 20 Ohms resistors that are connected in parallel.

<h3>How to achieve the desired resistance under these circumstances?</h3>

In order to achieve the desired resistance under the given circumstances, we would connect two 50 Ohms resistors in parallel and then connect it in series with the 20 Ohms resistors.

Mathematically, the total equivalence resistance of two resistors that are connected in parallel is given by:

1/Rt = 1/R₁ + 1/R₂

1/Rt = 1/50 + 1/50

1/Rt = 2/50

1/Rt = 1/25

Rt = 25 Ohms.

Next, we would connect this 25 Ohms resistor in series with the 20 Ohms resistor:

R₃ = 20 + Rt

R₃ = 20 + 25

R₃ = 45 Ohms.

In order to get a 35 Ohms resistance under the given circumstances, we would connect two 50 Ohms resistors in parallel and then connect it in series with two 20 Ohms resistors that are connected in parallel.

1/Rt = 1/R₁ + 1/R₂

1/Rt = 1/50 + 1/50

1/Rt = 2/50

1/Rt = 1/25

Rt = 25 Ohms.

1/R't = 1/R₁ + 1/R₂

1/R't = 1/20 + 1/20

1/R't = 2/20

1/R't = 1/10

R't = 10 Ohms.

Next, we would connect the 25 Ohms resistor in series with the 10 Ohms resistor:

R₃ = 10 + Rt