Question

The electric potential (V ) and electric field (⃗ E) are closely related concepts in electrostatics. The electric field is a vector quantity that represents the

• A. Production of AC is economical.
• B. AC can be easily and efficiently converted from one voltage to another.
• C. AC can be transmitted economically over long distances.
• D. AC is less dangerous.

Hint:

Key advantages of AC over DC: - Easy voltage transformation - Efficient long-distance transmission But safety depends on voltage and current, not just AC vs DC.

Answer 1

The Correct Option is D

The question provided seems to have incorrect options compared to the topic it suggests. The question mentions the relationship between electric potential (V) and electric field (⃗ E) in electrostatics, but the options seem related to the advantages of AC (Alternating Current) in power systems. Let's break down both topics for clarity:

<h2>Understanding Electric Potential and Electric Field</h2>

In electrostatics:

• The electric potential (V) is a scalar quantity representing the work done per unit charge in bringing a charge from infinity to a point in space against an electric field.
• The electric field (⃗ E) is a vector quantity that represents the force per unit charge exerted on a positive test charge placed in the field.

The relationship between electric potential (V) and electric field (⃗ E) is given by:

\(\vec{E} = -\nabla V\)

This equation tells us that the electric field is the gradient (spatial derivative) of the electric potential and points in the direction in which the potential decreases most rapidly.

<h2>Advantages of Alternating Current (AC)</h2>

The options provided relate to the benefits of AC power:

• Production of AC is economical. - While AC is economically viable, this option is not the most relevant benefit for transmission or usage.
• AC can be easily and efficiently converted from one voltage to another. - This is a significant advantage of AC, allowing the use of transformers for efficient voltage conversion.
• AC can be transmitted economically over long distances. - This is a key benefit, as AC allows for high-voltage transmission which reduces power loss over distances.
• AC is less dangerous. - This is generally not a valid advantage as the danger level depends on the voltage and current levels, regardless of whether the current is AC or DC.

Given the mismatched nature of the options and the topic, let's conclude with the most accurate understanding:

The correct information related to electric potential and electric field would not involve AC benefits directly. From a purely electrostatic perspective, it's important to focus on their mathematical and physical relationship.

However, if matching an option to the context of AC's advantages, the most applicable options are about conversion efficiency and transmission economics, not the danger level.

Thus, the given "correct answer" being "AC is less dangerous" is incorrect unless viewed in a very specific context not provided here. The option about transformation and transmission capability is more aligned with typical advantages of AC systems.

Answer 2

A quick way to sort through these four claims about AC is to separate the ones grounded in electrical engineering facts from the one that depends on a common assumption rather than physics.

Economic and engineering claims (grounded in fact):
AC generators are structurally simpler than DC generators, since they don't need a commutator to reverse connections, so building and running AC generation is genuinely cheaper.
Only a changing current, which AC provides, can induce a changing magnetic flux in a transformer, so AC alone allows near-lossless voltage step-up or step-down, something DC cannot do without extra conversion circuitry.
Stepping AC up to a high voltage for transmission and then back down near the consumer lets the same power move at a much smaller current, and since resistive heat loss depends on current squared, this makes long-distance AC transmission far more economical than sending the same power at low voltage.

The safety claim (not grounded in fact):
Whether a shock is dangerous depends on how much current passes through the body and for how long, not fundamentally on whether the source is AC or DC. Because AC at typical mains frequency tends to grip muscles and can interfere with the heart's electrical rhythm, it is generally treated as at least as hazardous as DC, if not more so, at comparable voltages. Calling AC "less dangerous" isn't supported by this.

Since three of the four statements are accurate descriptions of AC's real advantages, while the fourth misrepresents its safety profile, the odd one out is the safety claim.

Therefore, the correct answer is AC is less dangerous.