A step-down transformer operates a 2400v and
supplied a current of 60A. The turns ratio of the
transformer is 1/24. Calculate a)secondary voltage
b)primary current c)power output if the transformer
is 100% efficient?
The wording is poor. Does this mean "operates AT 2400v"....and is "SUPPLIED by a current of 60a" or " supplies a current of 60A" ?
If so, the secondary voltage is 100volts
if it supplies a 60 A current, then the primary current is 60/24 Amps
But with the wording, this problem is very flawed.
To calculate the values requested, we can use the formula for a transformer:
V₁ / V₂ = N₁ / N₂
Where:
V₁ = Primary voltage
V₂ = Secondary voltage
N₁ = Number of turns in the primary coil
N₂ = Number of turns in the secondary coil
a) Calculating the secondary voltage (V₂):
Given: V₁ = 2400V, turns ratio (N₁/N₂) = 1/24
Using the formula, we can rearrange it to solve for V₂:
V₁ / V₂ = N₁ / N₂
Substituting the known values:
2400 / V₂ = 1 / 24
Cross multiplying:
2400 * 24 = V₂
V₂ = 57600V
Therefore, the secondary voltage is 57600V.
b) Calculating the primary current (I₁):
Given: Secondary current (I₂) = 60A, turns ratio (N₁/N₂) = 1/24
The turns ratio does not affect the current, so the primary current will be the same as the secondary current.
Therefore, the primary current (I₁) is 60A.
c) Calculating the power output (P₂) if the transformer is 100% efficient:
Given: Power input (P₁) = Power output (P₂), turns ratio (N₁/N₂) = 1/24
The power is calculated using the formula:
P = IV
The input power (P₁) is equal to the output power (P₂) if the transformer is 100% efficient.
P₁ = P₂
Substituting the known values:
2400V * 60A = 57600V * I₂
144000W = 57600V * I₂
Dividing both sides by 57600V:
I₂ = 144000W / 57600V
I₂ = 2.5A
Therefore, the power output is 144000W if the transformer is 100% efficient.
To summarize:
a) The secondary voltage (V₂) is 57600V.
b) The primary current (I₁) is 60A.
c) The power output (P₂) is 144000W if the transformer is 100% efficient.