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 properties of resistors and how they behave in different configurations. Let's break down the steps to find the answer:
1. Series Connection:
When two resistors are connected in series, their resistances add up. If we consider the wires to behave as resistors, the total resistance (R_total) in a series circuit can be calculated by summing the individual resistances (R1 and R2).
R_total = R1 + R2
2. Parallel Connection:
When two resistors are connected in parallel, their reciprocals add up. In this case, consider the inverse of resistance, called conductance (G). The total conductance (G_total) in a parallel circuit can be calculated by adding the individual conductances (G1 and G2).
G_total = G1 + G2
Now, let's consider the energy produced, which is directly related to power. The power (P) can be calculated using Ohm's Law:
P = I^2 * R
where I is the current flowing through the wire and R is the resistance.
In both series and parallel connections, we can assume that the current flowing through each wire is the same. Therefore, the energy produced in series connection (E_series) and parallel connection (E_parallel) can be expressed as:
E_series = P_series = I^2 * R_total
E_parallel = P_parallel = I^2 * R_total'
Now, let's find the ratio of energy produced in the parallel connection to that in the series connection:
Ratio = E_parallel / E_series
= (I^2 * R_total') / (I^2 * R_total)
= R_total' / R_total
Since the wires are identical (same metal, same diameter, same length), their resistances are also the same:
R_total = R_total' = R
Therefore, the ratio becomes:
Ratio = R / R
= 1
So, the correct answer is A. 1:2