Final answer:
To find the effective resistance of resistors, you must know if they are in series or parallel. For parallel resistors, use the reciprocal sum method like in Option A to find 1.6 Ω. For series resistors, add them directly as in Option C to get 17 Ω.
Step-by-step explanation:
To calculate the effective resistance for a combination of resistors, you must first identify whether they are in series or parallel. The given resistances R1 = 3 Ω, R2 = 6 Ω, and R3 = 8 Ω have not been specified as being in series or parallel. However, we have been provided with several potential equations to determine the effective resistance:
Option A suggests they are in parallel: 1/R = 1/R1 + 1/R2 + 1/R3,
Option B suggests a multiplication of reciprocals which is not a method to find total resistance,
Option C implies that the resistors are in series: R = R1 + R2 + R3,
Option D suggests a multiplication of resistances, which also doesn't provide effective resistance in series or parallel.
The correct method to find the total resistance in parallel is similar to option A, but for series it is like option C. Assuming we are looking for a parallel combination based on the structure of Option A, we would calculate the reciprocal of the total resistance as follows:
1/R = 1/3 + 1/6 + 1/8
To solve this, we find a common denominator, which is 24, leading to:
1/R = 8/24 + 4/24 + 3/24 = 15/24
Now we simplify:
1/R = 5/8
And take the reciprocal of both sides to find the effective resistance:
R = 8/5 or 1.6 Ω
If the resistors are actually in series, the total resistance would simply be their sum:
R = R1 + R2 + R3 which equals 17 Ω.