Electricity is distributed from electrical substations to neighborhoods at 15,000 V. This is a 60 Hz oscillating (AC) voltage. Neighborhood transformers, seen on utility poles, step this voltage down to the 120 V that is delivered to your house. No energy is lost in an ideal transformer, so the output power P_out from the secondary coil equals the input power P_in to the primary coil. Suppose a neighborhood transformer delivers 250 A at 120 V. What is the current in the 15,000 V line from the substation?

Verified step by step guidance

1. Step 1: Understand the relationship between power and voltage in an ideal transformer. In an ideal transformer, the input power (Pin) to the primary coil equals the output power (Pout) from the secondary coil. The formula for power is given by: $P=VI$, where P is power, V is voltage, and I is current.
2. Step 2: Calculate the output power (Pout) from the secondary coil using the given values for voltage and current. The secondary coil delivers 120 V and 250 A, so the output power is: $P=VI=120\times 250$. This gives the total power delivered to the neighborhood.
3. Step 3: Since no energy is lost in an ideal transformer, the input power (Pin) to the primary coil is equal to the output power (Pout) from the secondary coil. Use the formula $P=VI$ to relate the input power to the primary coil's voltage and current.
4. Step 4: Rearrange the formula to solve for the current in the primary coil. The primary coil operates at 15,000 V, so the current in the primary coil is given by: $I=\frac{P}{V}$, where P is the input power (equal to the output power) and V is the primary coil voltage.
5. Step 5: Substitute the values for P (calculated in Step 2) and V (15,000 V) into the formula to find the current in the primary coil. This will give the current in the 15,000 V line from the substation.

Key Concepts

Transformers

Transformers are electrical devices that transfer electrical energy between two or more circuits through electromagnetic induction. They consist of primary and secondary coils, where the voltage can be stepped up or down based on the turns ratio of the coils. In an ideal transformer, the power input to the primary coil equals the power output from the secondary coil, allowing for efficient voltage conversion.

Power Conservation in Transformers

In an ideal transformer, the principle of power conservation states that the power entering the primary coil (P_in) is equal to the power exiting the secondary coil (P_out). This relationship can be expressed mathematically as P_in = V_in * I_in and P_out = V_out * I_out, where V is voltage and I is current. This concept is crucial for calculating the current in the primary circuit when the secondary circuit's parameters are known.

Ohm's Law

Ohm's Law is a fundamental principle in electrical engineering that relates voltage (V), current (I), and resistance (R) in a circuit. It states that V = I * R, meaning the current through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance. This law is essential for understanding how current behaves in electrical circuits, especially when analyzing transformers and their outputs.