1 Answer
A transformer is an electrical device that transfers electrical energy between two or more circuits through electromagnetic induction. It typically works by converting electrical energy from one voltage level to another, either stepping up (increasing) or stepping down (decreasing) the voltage. The formula used to describe the behavior of a transformer is based on its primary and secondary windings.
### Basic Transformer Formula
The basic formula for a transformer relates the primary and secondary voltages and currents to the number of turns in the primary and secondary coils:
\[
\frac{V_p}{V_s} = \frac{N_p}{N_s}
\]
Where:
- \(V_p\) is the voltage on the primary side (input voltage).
- \(V_s\) is the voltage on the secondary side (output voltage).
- \(N_p\) is the number of turns on the primary coil.
- \(N_s\) is the number of turns on the secondary coil.
This formula is known as the **turns ratio**. It tells you that the ratio of the primary voltage (\(V_p\)) to the secondary voltage (\(V_s\)) is directly proportional to the ratio of the number of turns in the primary coil (\(N_p\)) to the number of turns in the secondary coil (\(N_s\)).
### Step-Up and Step-Down Transformers
- **Step-up transformer**: When \(N_s > N_p\), the secondary voltage \(V_s\) will be higher than the primary voltage \(V_p\), and the transformer increases the voltage.
- **Step-down transformer**: When \(N_s < N_p\), the secondary voltage \(V_s\) will be lower than the primary voltage \(V_p\), and the transformer decreases the voltage.
### Relationship Between Current and Voltage
In an ideal transformer (where no energy is lost), the power on the primary side is equal to the power on the secondary side, which means:
\[
P_p = P_s
\]
Power is given by the formula:
\[
P = V \times I
\]
Where:
- \(P_p\) is the power on the primary side.
- \(P_s\) is the power on the secondary side.
- \(V\) is voltage.
- \(I\) is current.
Thus, we can write:
\[
V_p \times I_p = V_s \times I_s
\]
Where:
- \(I_p\) is the current on the primary side.
- \(I_s\) is the current on the secondary side.
Now, by combining this equation with the turns ratio formula, we get the relationship between the currents and the voltages:
\[
\frac{I_p}{I_s} = \frac{N_s}{N_p}
\]
This means that the ratio of primary current to secondary current is inversely proportional to the ratio of turns in the coils.
### Summary of Transformer Equations
1. **Voltage equation** (based on turns ratio):
\[
\frac{V_p}{V_s} = \frac{N_p}{N_s}
\]
2. **Current equation** (based on turns ratio):
\[
\frac{I_p}{I_s} = \frac{N_s}{N_p}
\]
3. **Power equation** (ideal transformer):
\[
V_p \times I_p = V_s \times I_s
\]
These equations are idealized for perfect transformers, where energy loss is neglected. In real transformers, factors such as resistance, core losses, and other inefficiencies may slightly alter these relationships, but these basic formulas still provide the fundamental understanding of how transformers work.
### Basic Transformer Formula
The basic formula for a transformer relates the primary and secondary voltages and currents to the number of turns in the primary and secondary coils:
\[
\frac{V_p}{V_s} = \frac{N_p}{N_s}
\]
Where:
- \(V_p\) is the voltage on the primary side (input voltage).
- \(V_s\) is the voltage on the secondary side (output voltage).
- \(N_p\) is the number of turns on the primary coil.
- \(N_s\) is the number of turns on the secondary coil.
This formula is known as the **turns ratio**. It tells you that the ratio of the primary voltage (\(V_p\)) to the secondary voltage (\(V_s\)) is directly proportional to the ratio of the number of turns in the primary coil (\(N_p\)) to the number of turns in the secondary coil (\(N_s\)).
### Step-Up and Step-Down Transformers
- **Step-up transformer**: When \(N_s > N_p\), the secondary voltage \(V_s\) will be higher than the primary voltage \(V_p\), and the transformer increases the voltage.
- **Step-down transformer**: When \(N_s < N_p\), the secondary voltage \(V_s\) will be lower than the primary voltage \(V_p\), and the transformer decreases the voltage.
### Relationship Between Current and Voltage
In an ideal transformer (where no energy is lost), the power on the primary side is equal to the power on the secondary side, which means:
\[
P_p = P_s
\]
Power is given by the formula:
\[
P = V \times I
\]
Where:
- \(P_p\) is the power on the primary side.
- \(P_s\) is the power on the secondary side.
- \(V\) is voltage.
- \(I\) is current.
Thus, we can write:
\[
V_p \times I_p = V_s \times I_s
\]
Where:
- \(I_p\) is the current on the primary side.
- \(I_s\) is the current on the secondary side.
Now, by combining this equation with the turns ratio formula, we get the relationship between the currents and the voltages:
\[
\frac{I_p}{I_s} = \frac{N_s}{N_p}
\]
This means that the ratio of primary current to secondary current is inversely proportional to the ratio of turns in the coils.
### Summary of Transformer Equations
1. **Voltage equation** (based on turns ratio):
\[
\frac{V_p}{V_s} = \frac{N_p}{N_s}
\]
2. **Current equation** (based on turns ratio):
\[
\frac{I_p}{I_s} = \frac{N_s}{N_p}
\]
3. **Power equation** (ideal transformer):
\[
V_p \times I_p = V_s \times I_s
\]
These equations are idealized for perfect transformers, where energy loss is neglected. In real transformers, factors such as resistance, core losses, and other inefficiencies may slightly alter these relationships, but these basic formulas still provide the fundamental understanding of how transformers work.