Question

Ohm's Law states that the potential difference across a device is equal to a) the current flowing through the device times the resistance of the device. b) the current flowing through the device divided by the resistance of the device. c) the resistance of the device divided by the current flowing through the device. d) the current flowing through the device times the crosssectional area of the device. e) the current flowing through the device times the length of the device.

Short answer

a) the current flowing through the device times the resistance of the device. b) the current flowing through the device divided by the resistance of the device. c) the resistance of the device divided by the current flowing through the device. d) the current flowing through the device times the cross-sectional area of the device. e) the current flowing through the device times the length of the device. Answer: a) the current flowing through the device times the resistance of the device.

Step-by-step solution

(Step 1: Analyze Statement a)

Statement a states that the potential difference across a device is equal to the current flowing through the device times the resistance of the device. According to Ohm's Law formula, \(V = IR\), this statement directly corresponds to the formula. We will consider this as a possible correct answer and check other statements for correctness.

(Step 2: Analyze Statement b)

Statement b states that the potential difference across a device is equal to the current flowing through the device divided by the resistance of the device. This statement would be represented by the formula \(V = \frac{I}{R}\). However, this is not the correct representation of Ohm's Law (\(V = IR\)), so statement b is incorrect.

(Step 3: Analyze Statement c)

Statement c states that the potential difference across a device is equal to the resistance of the device divided by the current flowing through the device. This statement would be represented by the formula \(V = \frac{R}{I}\). Just like statement b, this does not correspond to the correct formula of Ohm's Law (\(V = IR\)), so statement c is also incorrect.

(Step 4: Analyze Statement d)

Statement d states that the potential difference across a device is equal to the current flowing through the device times the crosssectional area of the device. Cross-sectional area is not related to Ohm's Law; it is more associated with the measurement of the wire's thickness. Since this statement does not comply with Ohm's Law formula (\(V = IR\)), statement d is incorrect.

(Step 5: Analyze Statement e)

Statement e states that the potential difference across a device is equal to the current flowing through the device times the length of the device. Length does play a role in determining resistance, but it is not directly related to the potential difference. This statement does not match the Ohm's Law formula (\(V = IR\)), so statement e is incorrect.

(Conclusion)

After analyzing each statement, we conclude that only Statement a correctly represents Ohm's Law. Therefore, the correct answer to this exercise is: \(a) \text{the current flowing through the device times the resistance of the device.}\)

Key concepts

Electrical Resistance

Electrical resistance is a fundamental concept in the field of electronics and physics, playing a crucial role in Ohm's Law. It measures how much an object resists the flow of electric current through it. Think of it like a narrow passage in a pipe limiting the water flow; similarly, resistance limits the flow of electric current. The unit of resistance is the ohm (\r), named after Georg Simon Ohm, who was the first to describe the relationship between voltage, current, and resistance.

Materials with high resistance make it harder for electrical current to flow, and those with low resistance allow current to flow more easily. Resistance is determined by the material's properties and its physical dimensions — the length, cross-sectional area, and temperature. For example, a long, thin wire has more resistance than a short, thick one of the same material.

The formula for resistance can be represented by: \(
R = \frac{V}{I}\),
where R is resistance, V is potential difference, and I is electric current. This equation is derived from Ohm's Law, which relates these three fundamental electrical quantities.

Potential Difference

Potential difference, often referred to as voltage, describes the work needed to move a unit of charge between two points in an electrical circuit. In simpler terms, it's the electric pressure that drives the flow of current, just as water pressure pushes water through a hose. Voltage is measured in volts (V), and a common analogy is to think of it as the height difference that lets water flow from higher to lower ground.

Within an electrical circuit, a power source, like a battery or generator, provides this potential difference which energizes the electrons to move through the conductor, thus creating an electric current. The greater the voltage, the more energy the electrons have, and the more current can potentially flow.

Ohm’s Law demonstrates the relationship as \(
V = IR\),
indicating that the potential difference (V) is proportional to the product of the current (I) and the resistance (R) in the circuit. When solving problems involving Ohm's Law, it is critical to identify the correct formulation to understand the behavior of electrical circuits.

Electric Current

Electric current is the flow of electric charge, carried by electrons, through a conductor like a wire. The standard unit for measuring electric current is the ampere (A), and it can be likened to the flow rate of water in a pipe.

There are two main types of current: direct current (DC), where electrons flow in one steady direction, and alternating current (AC), where electrons periodically change direction. Batteries provide DC, whereas AC is what you typically get from power outlets.

The amount of current that flows depends on the potential difference applied across the conductor and the resistance it encounters. Ohm's Law articulates this relationship with the simple formula: \(
I = \frac{V}{R}\).
This indicates that the current (I) is equal to the potential difference (V) divided by the resistance (R). In educational exercises, understanding this relationship can help students solve for unknown quantities in a circuit by rearranging the Ohm's Law formula as needed.