Let total no. of resistors in parallel be 'x' . ..

Total Resistance of resistors in parallel combination

= Total Resistance of all Combination - Resistance of Series combination...
so,R = Total resistance of parallel combination....

R=(6-5)ohm ..

R=1ohm...

[In Parallel combination R=(1/R1)+(1/R2)+....] [so, (1/5)+(1/5)+..... x times] ...

x(1/5) ohm = 1 ohm ...

x=5 ...

Problem Statement:

A resistor of 5 ohms is connected in series with a parallel combination of a number of resistors, each of 5 ohms. If the total resistance of the combination is 6 ohms, determine how many resistors are in parallel.

Solution:

To solve this problem, we can use the following steps:

Step 1: Identify the given information:
- The resistance of the resistor connected in series is 5 ohms.
- The resistance of each resistor in the parallel combination is also 5 ohms.
- The total resistance of the combination is 6 ohms.

Step 2: Understand the concept:
- When resistors are connected in series, the total resistance is the sum of individual resistances.
- When resistors are connected in parallel, the reciprocal of the total resistance is the sum of the reciprocals of individual resistances.

Step 3: Calculate the total resistance of the series and parallel combination:
- The total resistance of the series and parallel combination is given as 6 ohms.

Step 4: Calculate the resistance of the series combination:
- The resistance of the series combination is 5 ohms.

Step 5: Calculate the resistance of the parallel combination:
- To find the resistance of the parallel combination, we can use the formula:
1/Total Resistance = 1/R1 + 1/R2 + 1/R3 + ...
- Substituting the given values, we have:
1/6 = 1/5 + 1/R_parallel
- Solving for R_parallel, we get:
R_parallel = 30/7 ohms

Step 6: Calculate the number of resistors in parallel:
- Since each resistor in the parallel combination has a resistance of 5 ohms, we can divide the total resistance of the parallel combination by 5 to get the number of resistors in parallel:
Number of resistors in parallel = R_parallel / Resistance of each resistor
Number of resistors in parallel = (30/7) / 5
Number of resistors in parallel ≈ 0.857

Answer:
Approximately 0.857 resistors are in parallel. Since we cannot have fractional resistors, we can conclude that there is 1 resistor in parallel.