Two wires if the same metal and of the same dia. And same length are connected in series 1st n then parallel, the ratio of energy produced during series n parallel connection will be .....
A. 1:2
B. 2:1
C. 1:4
D. 4:1
To determine the ratio of energy produced during series and parallel connection of two wires, we need to consider the concept of electrical resistance and power.
1. Series Connection:
In a series connection, the total resistance (R) is equal to the sum of the individual resistances (R₁ and R₂) of the two wires.
Therefore, the total resistance (R) is given by the formula:
R = R₁ + R₂
The power (P) dissipated in a circuit can be calculated using the formula:
P = V²/R
where V is the voltage across the circuit and R is the resistance.
Since the voltage (V) across the series connection is constant, for both wires, the power can be written as:
P = V²/(R₁ + R₂)
2. Parallel Connection:
In a parallel connection, the total resistance (R) is given by the reciprocal of the sum of the reciprocals of individual resistances (1/R₁ and 1/R₂) of the two wires:
1/R = 1/R₁ + 1/R₂
The power (P) dissipated in a circuit can be calculated using the formula:
P = V²/R
where V is the voltage across the circuit and R is the resistance.
Since the voltage (V) across the parallel connection is constant, for both wires, the power can be written as:
P = V²/(1/R₁ + 1/R₂)
Now, to find the ratio of energy produced during series and parallel connection, we can compare the powers in the two cases.
Let's assume the resistance, length, and diameter of both wires are the same.
For the series connection: Pseries = V²/(R₁ + R₂)
For the parallel connection: Pparallel = V²/(1/R₁ + 1/R₂)
To simplify the comparison, let's assume that R₁ = R₂ = R. This assumption means that both wires have the same resistance.
Pseries = V²/(R + R) = V²/(2R)
Pparallel = V²/(1/R + 1/R) = V²/(2/R) = V²R/2
Therefore, the ratio of energy produced during series and parallel connection is Pseries/Pparallel = (V²/(2R))/(V²R/2) = 1:1
So, the correct answer is not provided in the given options (A, B, C, or D).