Animated Solution for Physics - Electromagnetic Induction: Comprehension Passage

Imagine a massive thermal power plant generating a staggering $600\text{ kW}$ of electrical power. This energy needs to travel $20\text{ km}$ to reach consumers. But how do we get it there efficiently? We have two choices: send it directly through cables, or use transformers to manipulate the voltage. Let's explore why the latter is the undisputed champion of modern electrical grids.

If we decide to transmit the power directly at the generated voltage of $4000\text{ V}$, we first need to determine the current flowing through the cables. Using the fundamental power equation $P=VI$, we can isolate the current:

That is a massive amount of current! Now, let's look at the cables. The resistance of the cable is given as $0.4\Omega /\text{km}$. Over a distance of $20\text{ km}$, the total resistance $R$ becomes:

When current flows through a resistance, energy is inevitably lost as heat. This is governed by Joule's Law of Heating, $P_{\text{loss}}=I^{2}R$. Let's plug in our numbers:

Out of the $600\text{ kW}$ generated, $180\text{ kW}$ is completely wasted just heating up the wires! To put this into perspective, let's calculate the percentage loss:

Losing $30\%$ of your product before it even reaches the customer is an engineering nightmare. This is exactly why direct transmission at low voltages is never used for long distances.

To combat this massive energy loss, we introduce transformers. The key to reducing power loss ($I^{2}R$) is to drastically reduce the current ($I$). Since $P=VI$, if we step up the voltage ($V$), the current ($I$) must drop proportionally to transmit the same power.

At the power plant, a step-up transformer is employed with a primary to secondary turns ratio of $1:10$. Because the voltage ratio is equal to the turns ratio ($\frac{V_p}{V_s}=\frac{N_p}{N_s}$), the secondary voltage becomes:

By stepping the voltage up to $40000\text{ V}$, the current drops to a mere $15\text{ A}$. The new power loss would be $(15{)}^2\times 8=1800\text{ W}$, or just $1.8\text{ kW}$—a staggering improvement from $180\text{ kW}$!

While $40000\text{ V}$ is fantastic for efficient transmission, it is incredibly dangerous for household appliances. Therefore, at the consumers' end, we must use a step-down transformer to bring the voltage back down to a safe $200\text{ V}$.

We know the input voltage to this step-down transformer is $40000\text{ V}$, and the required output is $200\text{ V}$. We can easily find the required turns ratio:

Thus, the step-down transformer must have a primary to secondary turns ratio of $200:1$. This elegant dance of stepping voltage up for the journey and down for the destination is the backbone of the global electrical grid.