A transformer has 25 turns in the primary coil and 200 turns in the secondary coil. If 12 V is connected to the primary coil and a 20-Ω device is connected to the secondary coil, calculate the current in Amperes passing through the device.
Vs = 200/25 * 12=96 V.=Secondary voltage
I = Vs/20 = 96/20 = 4.8 Amps.
To calculate the current passing through the device, we need to use the formula for the current in a transformer:
I_secondary = (V_primary / V_secondary) * I_primary
Where:
I_secondary is the current in the secondary coil
V_primary is the voltage across the primary coil
V_secondary is the voltage across the secondary coil
I_primary is the current in the primary coil
We are given that the primary voltage (V_primary) is 12 V, so let's calculate the secondary voltage (V_secondary) using the turns ratio:
Turns ratio = N_primary / N_secondary
where:
N_primary is the number of turns in the primary coil (25 turns)
N_secondary is the number of turns in the secondary coil (200 turns)
Turns ratio = 25 / 200 = 1/8
Now, let's calculate the secondary voltage:
V_secondary = V_primary * Turns ratio
V_secondary = 12 V * (1/8) = 1.5 V
Substitute the values into the current formula:
I_secondary = (V_primary / V_secondary) * I_primary
I_secondary = (12 V / 1.5 V) * I_primary
We know that the secondary resistance is 20 Ω and Ohm's law states that V = I * R, so the current in the secondary coil is:
I_secondary = V_secondary / R_secondary
I_secondary = 1.5 V / 20 Ω = 0.075 A
Therefore, the current passing through the device connected to the secondary coil is 0.075 Amperes.
To calculate the current passing through the device, we can use the formula for calculating the current in a circuit, which is:
I = V / R
Where:
I is the current in Amperes,
V is the voltage across the circuit, and
R is the resistance of the circuit.
Here's how we can calculate the current passing through the device:
1. First, we need to find the voltage across the secondary coil. This can be determined using the turns ratio of the transformer.
The turns ratio is given by:
Turns ratio = number of turns in secondary coil / number of turns in primary coil
In this case, the turns ratio is:
Turns ratio = 200 / 25 = 8
So, the voltage across the secondary coil is 8 times the voltage across the primary coil, which is 12 V.
2. Now, we can calculate the current using Ohm's Law.
The voltage across the secondary coil is 12 V (found in step 1), and the resistance of the device connected to the secondary coil is 20 Ω.
I = V / R
= 12 V / 20 Ω
= 0.6 A
Therefore, the current passing through the device is 0.6 Amperes.