In a transformer, number of turns in the primary are 140 and that in the secondary are 280. If curre

Q: Why is the current inversely proportional to the number of turns?

In an ideal transformer, the input power equals the output power ($V_p I_p = V_s I_s$). Since voltage is directly proportional to the number of turns ($V_p / V_s = N_p / N_s$), the current must be inversely proportional to maintain constant power.

Q: Does this mean a step-up transformer decreases the current?

Yes! A step-up transformer increases the voltage, which means it must decrease the current to ensure that energy is conserved.

Q: What if the transformer is not ideal?

If the transformer is not ideal, there are power losses (like heat or eddy currents). In that case, the output power is less than the input power, and you would need to account for the efficiency ($\eta$) using the formula $\eta V_p I_p = V_s I_s$.

Q: Can a transformer work with direct current (DC)?

No, transformers rely on electromagnetic induction, which requires a changing magnetic field. A steady DC current creates a constant magnetic field, so no voltage would be induced in the secondary coil.

Q: Why do we use transformers in power transmission?

Transformers allow us to step up the voltage for long-distance transmission, which significantly reduces the current. Lower current means less power lost as heat ($I^2 R$ losses) in the transmission wires.

Question

In a transformer, number of turns in the primary are $140$ and that in the secondary are $280$. If current in primary is $4	ext{ A}$, then that in the secondary is

Options:

(A) $4	ext{ A}$

(B) $2	ext{ A}$

(C) $6	ext{ A}$

(D) $10	ext{ A}$

Sigma Percentile · Accepted Answer

### Analyzing the Setup
Imagine you are looking at a transformer, the unsung hero of our electrical grid. It consists of two coils wrapped around a magnetic core. The primary coil is where the electrical energy enters, and the secondary coil is where it exits.

In our specific problem, the primary coil has $N_p = 140$ turns and carries a current of $I_p = 4 	ext{ A}$. The secondary coil, on the other hand, has $N_s = 280$ turns. Our mission is to find the current flowing through this secondary coil, $I_s$.

### The Master Equation
To solve this, we need to understand the heart of an ideal transformer: **Conservation of Energy**. Assuming no power is lost as heat or magnetic leakage, the power entering the primary coil equals the power leaving the secondary coil.

Since electrical power is the product of voltage and current ($P = VI$), we can write:
$$V_p I_p = V_s I_s$$

We also know from Faraday's Law of Induction that the voltage across a coil is directly proportional to its number of turns. Therefore, the ratio of voltages is equal to the ratio of turns:
$$\frac{V_s}{V_p} = \frac{N_s}{N_p}$$

By combining these two principles, we discover a beautiful inverse relationship between current and the number of turns. If the voltage goes up, the current must go down to keep the power constant. This gives us our master equation:
$$\frac{I_p}{I_s} = \frac{N_s}{N_p}$$

### Final Calculation
Now, let's bring our known values into this elegant equation. We substitute $I_p = 4$, $N_s = 280$, and $N_p = 140$:
$$\frac{4}{I_s} = \frac{280}{140}$$

Notice how the right side of the equation simplifies beautifully. Two hundred and eighty is exactly twice one hundred and forty:
$$\frac{4}{I_s} = 2$$

With a quick rearrangement, we can isolate our unknown secondary current:
$$I_s = \frac{4}{2}$$
$$I_s = 2 	ext{ A}$$

**The current in the secondary coil is exactly 2 A.**

This makes perfect physical sense! The secondary coil has twice as many turns as the primary coil, meaning it steps up the voltage by a factor of two. To conserve energy, it must step down the current by the exact same factor. The physics is perfectly balanced!

Animated Solution for Physics - Electromagnetic Induction: In a transformer, number of turns in the primary are $140$ and that in the secondary are $280$ . If current in primary is $4 A$ , then that in the secondary is

Select Answer:

Visualized Solution

Visualizing the Transformer

The Transformer Equation

Substituting the Values

Simplifying the Ratio

Calculating Secondary Current

Food for Thought

The Sigma Insight: Alternating Current (AC) and Voltage

Analyzing the Setup Imagine you are looking at a transformer, the unsung hero of our electrical grid

The Master Equation To solve this, we need to understand the heart of an ideal transformer: Conservation of Energy

Final Calculation Now, let's bring our known values into this elegant equation

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