(2) 1500 Ù resistors are connected in series. They are then connected in parallel to a single (1)
5 kÙ resistor.
a) Draw the circuit before and after reduction:
b) What is the equivalent resistance of the circuit?
R1 = 1.5K Ohms
R2 = 1.5K Ohms.
R3 = 5K Ohms.
R1 + R2 = 1.5K + 1.5K = 3K.
Req = 3k*5k / (3k + 5k) = 15k / 8k = 1.875k = 1875 Ohms.
a) To draw the circuit before and after reduction, we first need to understand how resistors are connected in series and parallel.
In a series connection, the resistors are connected one after the other, like a chain. The current flows through each resistor in the same order. To draw the circuit before reduction, we can represent the two 1500 Ù resistors in series as follows:
---1500 Ù---1500 Ù---
In a parallel connection, the resistors are connected to the same two points. The current splits among the resistors in parallel. To draw the circuit after reduction, we can represent the two 1500 Ù resistors connected in parallel to the 5 kÙ resistor as follows:
----1500 Ù----
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----1500 Ù----
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----5 kÙ-----
b) To find the equivalent resistance of the circuit, we need to simplify it by using the formulas for resistors connected in series and parallel.
For resistors connected in series, the total resistance (RT) is equal to the sum of each individual resistance (R1, R2, R3, ...):
RT = R1 + R2 + R3 + ...
For resistors connected in parallel, the reciprocals of the resistances add up to the reciprocal of the total resistance:
1/RT = 1/R1 + 1/R2 + 1/R3 + ...
First, let's simplify the two 1500 Ù resistors connected in series:
RT_series = R1 + R2
= 1500 Ù + 1500 Ù
= 3000 Ù
Now, we can find the equivalent resistance when the two 1500 Ù resistors connected in series are connected in parallel to the 5 kÙ resistor:
1/RT_parallel = 1/RT_series + 1/R3
= 1/3000 Ù + 1/5000 Ù
To combine these fractions, we need a common denominator:
1/RT_parallel = (1/3000 Ù) * (5000 Ù/5000 Ù) + (1/5000 Ù) * (3000 Ù/3000 Ù)
= 5000 Ù / (3000 Ù * 5000 Ù) + 3000 Ù / (5000 Ù * 3000 Ù)
= 5000 Ù + 3000 Ù / 15,000,000 Ù² + 15,000,000 Ù²
= 8000 Ù / 15,000,000 Ù²
Taking the reciprocal of both sides, we get:
RT_parallel = 15,000,000 Ù² / 8000 Ù
= 1875 Ù
Therefore, the equivalent resistance of the circuit is 1875 Ù.