A step-up transformer used in a car has a potential difference of 10 V across the primary coil with 12 turns. What is the current in the secondary coil of resistance 2.5 Ω if the number of turns in the secondary coil is 54 turns?
Using the equation, we can find the emf across the secondary coil.
Ns/Np = Vs/Vp
Vs = Vp(Ns/Np)
Vs = 10(54/12)
Vs = 45V
I = 45/2.5
I = 18 A
To find the current in the secondary coil of a step-up transformer, we need to use the transformer equation:
Vp / Vs = Np / Ns
Where:
Vp is the potential difference across the primary coil,
Vs is the potential difference across the secondary coil,
Np is the number of turns in the primary coil,
Ns is the number of turns in the secondary coil.
First, let's substitute the known values into the equation:
10 V / Vs = 12 / 54
To solve for Vs, we can cross-multiply and then isolate the variable:
10 V * 54 = 12 * Vs
540 V = 12 * Vs
Vs = (540 V) / 12
Vs = 45 V
Now that we have the potential difference across the secondary coil (Vs), we can find the current using Ohm's law:
I = V / R
Where:
I is the current,
V is the potential difference,
R is the resistance.
Substituting the values into the equation:
I = 45 V / 2.5 Ω
I = 18 A
Therefore, the current in the secondary coil is 18 Amperes.
To find the current in the secondary coil, we need to first determine the voltage across the secondary coil using the turns ratio.
Given:
Potential difference across the primary coil (Vp) = 10 V
Number of turns in the primary coil (Np) = 12 turns
Number of turns in the secondary coil (Ns) = 54 turns
Resistance of the secondary coil (Rs) = 2.5 Ω
Step 1: Find the turns ratio (Np / Ns)
Turns ratio (Np / Ns) = 12 / 54 = 1/4.5
Step 2: Calculate the voltage across the secondary coil (Vs)
Vs = Vp × (Np / Ns) = 10 V × (1/4.5) = 2.22 V
Step 3: Calculate the current in the secondary coil (Is)
Using Ohm's Law: Is = Vs / Rs = 2.22 V / 2.5 Ω ≈ 0.89 A
Thus, the current in the secondary coil is approximately 0.89 Amperes.