in a circuit two resistors of 100 ohm and 80 ohm are connected in parallel. The parallel group is then connected in series with a 100 ohm resistor what is the total resistance of the circuit
When resistors are connected in parallel, the total resistance is given by the formula:
1/𝑅𝑡𝑜𝑡𝑎𝑙 = 1/𝑅1 + 1/𝑅2
Where 𝑅1 and 𝑅2 are the resistances of the two resistors.
Let's calculate the total resistance of the parallel group:
1/𝑅𝑡𝑜𝑡𝑎𝑙 = 1/100 + 1/80
1/𝑅𝑡𝑜𝑡𝑎𝑙 = 0.01 + 0.0125
1/𝑅𝑡𝑜𝑡𝑎𝑙 = 0.0225
Now, let's calculate the total resistance of the circuit when the parallel group is connected in series with a 100 ohm resistor:
𝑅𝑡𝑜𝑡𝑎𝑙 = 100 + 100
𝑅𝑡𝑜𝑡𝑎𝑙 = 200 ohms
Therefore, the total resistance of the circuit is 200 ohms.
To find the total resistance of the circuit, we need to find the equivalent resistance of the parallel group (100 ohm and 80 ohm resistors) first.
In a parallel combination, the reciprocal of the equivalent resistance (R_parallel) is equal to the sum of the reciprocals of the individual resistances (R1 and R2).
So, 1/R_parallel = 1/R1 + 1/R2
For R1 = 100 ohm and R2 = 80 ohm:
1/R_parallel = 1/100 + 1/80
To add the fractions, we need to find a common denominator:
1/R_parallel = 80/8000 + 100/8000
1/R_parallel = 180/8000
Simplifying it further:
1/R_parallel = 9/400
Now, taking the reciprocal of both sides:
R_parallel = 400/9 ≈ 44.44 ohm
Now, we need to find the equivalent resistance when this parallel combination is in series with a 100 ohm resistor.
In a series combination, the total resistance (R_total) is equal to the sum of the individual resistances:
R_total = R_parallel + R3
Given R_parallel = 44.44 ohm and R3 = 100 ohm:
R_total = 44.44 + 100 = 144.44 ohm
Therefore, the total resistance of the circuit is approximately 144.44 ohm.
To find the total resistance of the circuit, we need to apply the principles of series and parallel resistors.
First, let's consider the two resistors in parallel. In a parallel configuration, the reciprocal of the total resistance (1/R_total) is equal to the sum of the reciprocals of the individual resistances (1/R_1 + 1/R_2).
In this case, R_1 is 100 ohms and R_2 is 80 ohms. So, the reciprocal of the total resistance of the parallel resistors (1/R_p) is:
1/R_p = 1/R_1 + 1/R_2
1/R_p = 1/100 + 1/80
1/R_p = (80 + 100)/(100 * 80)
1/R_p = 180/8000
1/R_p = 0.0225
Taking the reciprocal of 0.0225 gives us the total resistance of the parallel resistors:
R_p = 1/0.0225
R_p = 44.44 ohms (approximately)
Now, we have a series combination of the parallel resistors and a 100 ohm resistor. In a series configuration, the total resistance (R_total) is equal to the sum of the individual resistances.
So, the total resistance of the circuit is:
R_total = R_p + R_3 (where R_3 is the third resistor, which is 100 ohms)
R_total = 44.44 + 100
R_total = 144.44 ohms (approximately)
Therefore, the total resistance of the circuit is approximately 144.44 ohms.