Resistance of n Resistors in Series & Parallel: Solve n,N & R

[metz143]

Question 1: A group of n resistors each of resistance R, are connected in series. What is the total resistance?What is the total resistance if the resistors are connected in parallel?

Questions 2: A series-parallel group of resistors each of resistance R, have n equal resistances in series, in each of N row in parallel. What is the total resistance?(express your answer for 1 and 2 in terms of n,N & R);

 

[TenaliRaman]

I guess u are at the start of your electrical theory and just learned Ohm's Law.

Ok we will go slow. Start with the n Resistors in series problem.

1> We have a circuit with n resistors each of resistance R connected in series. Let's say we connect a battery of voltage V to this circuit which drives a current I through the circuit.
2> Can u find the voltage across each resistor?
3> Once u are done with step 2, let's rip out all the resistance and replace it with a single equivalent resistor (lets call it Req).
4> Again we have the same setup, a battery of voltage V driving current I through the circuit. What is the voltage across Req?
5> What is the relationship between the voltages u found in step 2 and the voltage u found in step 4?
6> Once u are finished with step5, the answer is immediately seen ... if not post your working and we will help u further.

-- AI

 

[wais]

Question 1:

When resistors are connected in series, the total resistance is equal to the sum of individual resistances. Therefore, for n resistors in series, the total resistance (Rs) can be expressed as:

Rs = nR

On the other hand, when resistors are connected in parallel, the total resistance is given by the reciprocal of the sum of reciprocals of individual resistances. For n resistors in parallel, the total resistance (Rp) can be expressed as:

Rp = 1/(1/R + 1/R + ... + 1/R) = 1/(n/R) = R/n

Question 2:

In a series-parallel group, the resistors are arranged in a combination of series and parallel connections. In this case, the total resistance (Rt) can be calculated by first finding the equivalent resistance of each row in parallel and then adding them in series. This can be expressed as:

Rt = (nR/N) + (nR/N) + ... + (nR/N) = (nR/N) * N = nR

Therefore, the total resistance in this case is also given by nR. This is because the number of resistors (n) and the resistance of each resistor (R) are the same in both series and parallel connections.

In summary, the total resistance for n resistors in series is nR, while for n resistors in parallel it is R/n. And for a series-parallel combination of n resistors with N rows in parallel, the total resistance is also nR.