# Ohm's Law and AC Power: Explaining the Paradox

• waqarrashid33
In summary, the conversation discusses the relationships between P, I, R, and V and how they are affected by different voltages and currents. It explains that P=IV is not an inverse relationship between I and V, but rather a calculation for power. The issue of supplying a consumer with the same power at different voltages is also addressed, and it is noted that the consumer must have different resistances in each case. The conversation also mentions the use of transformers to adjust voltage for end-users, which changes the effective resistance of the consumer.
waqarrashid33
I am confuse at a point that is:
I equation P=IV there is an inverse relation between I and V But according to ohm law there is direct relation between I and V.

How in in ac Power transmission line 1100 volt cause small current than 220 volt...

Everyone got confused when i ask this question..

You have four variables, P, I, R and V and two relations.
P = IV
V = IR

choose the values of any two variables, and you can compute the other two.

Note that you can only combine the two relations if they both deal with the same resistance.
If you have 1100 volt and a small current, and than 220 Volt with a larger current, these voltages and currents must be across different resistances.

i mean here when we step up 220 volt then current is reduced and voltage is increased...

It is generally wrong to describe P = IV as an inverse relationship between I and V. It would be right only if P were a constant.

In the 'usual' case of applying a p.d. V to a resistor of constant resistance R (i.e. the resistor obeys Ohm's law), if you double V, you will double I, and P (= IV) will go up by a factor of 4. So whatever you do to V, I will change proportionately, and P won't be constant, so P = IV doesn't give a relationship between I and V, it is simply a recipe for calculating P.

Your problem arises, I believe, because you've been required to consider how to get a given amount of power to a 'consumer'. And, using P = IV, you've thought 100 A and 10000 V would do just as well as 1000 A and 1000 V. This is true, but note that to take a current of 100 A at a p.d. of 10000 V, the consumer would have to have a resistance of 100 ohm, whereas to take a current of 1000 A at a p.d. of 1000V, the consumer would have to have a resistance of 1 ohm. So if we're considering ways of supplying the consumer with the same power at different voltages, the consumer must have different resistances in each case. That's why Ohm's law isn't applicable to the consumer in this type of calculation.

[Warning what follows is a bit compact and could cause (more?) confusion. If in doubt, I suggest you don't read it.] You might well ask: don't the end-users want a fixed voltage (110 V or 230 V or whatever)? Yes. What I've called 'the consumer' is in fact the input side of a transformer which steps the voltage down for the end users. A different transformer would have to be used if the transmission voltage going to the input of the transformer were changed. This changes the effective resistance of the consumer.

Ohm's Law states that the current (I) flowing through a conductor is directly proportional to the voltage (V) applied across it, and inversely proportional to the resistance (R) of the conductor. This relationship is expressed as I = V/R. Therefore, as the voltage increases, the current also increases, and as the resistance increases, the current decreases.

However, when we consider AC power transmission, we must also take into account the concept of reactance. In AC circuits, the voltage and current are constantly changing direction, which leads to the concept of impedance, which is the overall opposition to the flow of current in an AC circuit. This impedance is made up of two components: resistance and reactance.

In AC circuits, the voltage and current are not always in phase, meaning they do not peak at the same time. This results in a phase difference between the two, leading to a decrease in the effective voltage and current values. This is known as the power factor, and it is expressed as the cosine of the phase angle between voltage and current.

Now, when we consider the transmission of power, we must also take into account the losses that occur in the transmission lines. At higher voltages, the losses due to resistance are lower compared to lower voltages. This means that even though the current may be smaller at 1100 volts compared to 220 volts, the power loss due to resistance will be lower at 1100 volts. Therefore, higher voltage transmission lines are more efficient in terms of power loss.

In conclusion, the apparent paradox of higher voltage leading to smaller current in AC power transmission lines can be explained by considering the concepts of reactance, power factor, and power loss. These factors play a significant role in determining the efficiency of power transmission and must be taken into account when analyzing Ohm's Law in AC circuits.

## What is Ohm's Law?

Ohm's Law is a fundamental principle in physics that describes the relationship between voltage, current, and resistance in an electrical circuit. It states that the current through a conductor between two points is directly proportional to the voltage across the two points, and inversely proportional to the resistance between them.

## How do you calculate voltage, current, and resistance using Ohm's Law?

To calculate voltage, current, or resistance using Ohm's Law, simply use the formula V=IR, where V stands for voltage, I stands for current, and R stands for resistance. For example, if you have a circuit with a resistance of 10 ohms and a current of 2 amps, the voltage would be 20 volts (V=10ohms x 2amps).

## What is the paradox of AC power in relation to Ohm's Law?

The paradox of AC power is that, according to Ohm's Law, the current and voltage in an AC circuit should be in phase with each other. However, in reality, the voltage and current are often out of phase, which means they do not occur at the same time. This can be confusing because it goes against what Ohm's Law predicts.

## How is the paradox of AC power explained?

The paradox of AC power can be explained by the concept of reactance, which is the opposition to the flow of current in an AC circuit due to capacitance or inductance. In an AC circuit, the voltage and current are not always in phase because of the effects of reactance. This means that the voltage and current may not occur at the same time, but they are still related according to Ohm's Law.

## Why is understanding Ohm's Law and AC power important?

Understanding Ohm's Law and AC power is crucial for anyone working with electrical circuits, such as scientists, engineers, and electricians. It allows us to accurately calculate and measure voltage, current, and resistance in a circuit, and helps us troubleshoot and solve problems when they arise. Additionally, understanding the paradox of AC power can help us better understand and design more efficient electrical systems.

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