A transformer consists of 275 primary windings and 834 secondary windings. If the potential difference across the primary coil is 25 V, (a) What is the voltage across the secondary coil? (b) what is the effective load resistance of the secondary coil if it is connected across a 125 ohm resistor.
Ok I got part (a) as being 75.82 V...but I am totally confused on part b I don't know what it is asking for or any equation that would work for it! Help please!
To solve part (b) and find the effective load resistance of the secondary coil, we can use the turns ratio and the formula for voltage transformation in a transformer.
Given:
Number of primary windings (N1) = 275
Number of secondary windings (N2) = 834
Voltage across primary coil (V1) = 25 V
Load resistance (R_load) = 125 Ω
The turns ratio (n) is given by:
n = N2 / N1
In this case, n = 834 / 275
(a) Voltage across the secondary coil (V2) can be calculated using the turns ratio:
V2 = V1 * n
Substituting the given values in, we have:
V2 = 25 V * (834 / 275)
V2 = 75.82 V (as you correctly calculated)
Now, let's move on to part (b):
The formula for voltage transformation in a transformer is:
V2 / V1 = N2 / N1
We can rearrange this equation to solve for N2:
N2 = (V2 / V1) * N1
Now, let's substitute the known values and solve for N2:
N2 = (75.82 V / 25 V) * 275
Hence, N2 = 831.01 (approximately)
Since we cannot have fractional turns, we can round N2 to the nearest whole number and use it to calculate the effective load resistance (R_load_effective):
R_load_effective = (N2 / N1)^2 * R_load
Substituting the known values in, we get:
R_load_effective = (831 / 275)^2 * 125 Ω
R_load_effective = 846.42 Ω (approximately)
Therefore, the effective load resistance of the secondary coil when connected across a 125 Ω resistor is approximately 846.42 Ω.
To solve part (b) of the question, we need to determine the effective load resistance of the secondary coil when it is connected across a 125-ohm resistor.
To find the effective load resistance, we first need to understand the concept of a transformer's turns ratio. The turns ratio is the ratio of the number of turns in the primary coil (N₁) to the number of turns in the secondary coil (N₂). In this case, the transformer has 275 primary windings (N₁) and 834 secondary windings (N₂).
The turns ratio (TR) can be calculated as follows:
TR = N₂ / N₁
In this case, TR = 834 / 275 = 3.0364 (rounded to four decimal places).
The voltage ratio (VR) is equal to the turns ratio. In other words, VR = TR.
So, in part (a), we found that the voltage across the primary coil (V₁) is 25 volts. Using the voltage ratio, we can calculate the voltage across the secondary coil (V₂) as follows:
V₂ = V₁ × TR
Substituting the values, V₂ = 25 V × 3.0364 ≈ 75.91 V (rounded to two decimal places).
Now, let's move on to part (b), which asks for the effective load resistance of the secondary coil when it is connected across a 125-ohm resistor.
The effective load resistance (R_eff) in the secondary coil is related to the load resistance (R_load) by the following formula:
R_eff = (VR)² × R_load
In this case, the voltage ratio (VR) is 3.0364 (rounded to four decimal places), and the load resistance (R_load) is 125 ohms (as given in the question). We can substitute these values into the formula to calculate the effective load resistance:
R_eff = (3.0364)² × 125 Ω
R_eff = 9.2194 × 125 Ω
R_eff ≈ 1152.43 Ω (rounded to two decimal places).
Therefore, the effective load resistance of the secondary coil, when connected across a 125-ohm resistor, is approximately 1152.43 ohms.