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Ohm's law states that electrical current is inversely Lassen Volkanic National Park proportional to the resistance. A current of 18 amperes is flowing through a conductor whose resistance is \(4 \mathrm{ohms}\). a. What is the current that flows through the system if the resistance is \(8 \mathrm{ohms}\) ? b. What is the resistance of the conductor if a current of 12 amperes is flowing?

Short Answer

Expert verified
a. 9 amperes b. 6 ohms

Step by step solution

01

Understand Ohm's Law

Ohm's Law is given by the formula \( V = I \cdot R \), where \( V \) is the voltage, \( I \) is the current, and \( R \) is the resistance. We can express current as \( I = \frac{V}{R} \), so current is inversely proportional to resistance for a constant voltage.
02

Calculate Voltage for Resistance of 4 ohms

Given that \( I = 18 \) amperes and \( R = 4 \) ohms, we can find the voltage: \( V = I \cdot R = 18 \times 4 = 72 \) volts.
03

Calculate Current for Resistance of 8 ohms

The voltage remains the same at 72 volts. Use the formula \( I = \frac{V}{R} \) with \( R = 8 \) ohms: \( I = \frac{72}{8} = 9 \) amperes.
04

Calculate Resistance for Current of 12 amperes

Use the known voltage of 72 volts and \( I = 12 \) amperes to find the resistance: \( R = \frac{V}{I} = \frac{72}{12} = 6 \) ohms.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Electrical Current
Electrical current is the flow of electric charge. In most cases, this charge is carried by electrons in a conductor, such as a wire. Current is measured in amperes (A), often simply referred to as "amps." One ampere is equal to the flow of one coulomb of charge per second. To visualize this, think of electrical current as water flowing through a pipe, where more water translates to a stronger flow.
Understanding the behavior of electrical current is essential because it helps determine how much energy is being used in an electronic circuit. When analyzing circuits, Ohm's Law is an invaluable tool.
Using the formula from Ohm's Law, current (I) can be calculated if the voltage (V) and resistance (R) are known, by rearranging the equation to: \( I = \frac{V}{R} \).
  • Current results in energy usage
  • Measured in amperes
  • Directly calculated using voltage and resistance
Resistance Calculation
Resistance is a measure of how much an object opposes the flow of electric current. It is analogous to the narrowing of a pipe which restricts water flow, causing a reduction in current.
Resistance is measured in ohms (Ω), and high resistance implies less current can flow at a given voltage. Resistance in a conductor varies based on material, temperature, and physical dimensions, among other factors.
To find resistance using Ohm's Law, you can rearrange the equation to \( R = \frac{V}{I} \), where V is voltage and I is current.
Effective resistance calculation ensures components are used safely and circuits operate as intended. For example, if we know voltage is 72 volts and current is 12 amperes, the resistance is \( R = \frac{72}{12} = 6 \) ohms.
  • Measured in ohms (Ω)
  • Affects current flow
  • Calculated as \( R = \frac{V}{I} \)
Voltage
Voltage can be thought of as the electrical pressure that pushes electric current through a circuit. It is the difference in electric potential energy between two points in a circuit. Voltage is measured in volts (V).
This pressure causes the current to flow, similar to how pumps create water flow in a plumbing system. High voltage means a strong potential to push current, enabling more robust performance in electronic devices if properly managed.
In Ohm's Law, voltage is expressed as \( V = I \cdot R \), indicating what happens when there are changes in current or resistance.
Knowing the voltage in a circuit helps in determining both current and resistance. For example, if I is 18 amperes and R is 4 ohms, then \( V = 18 \times 4 = 72 \) volts.
  • Measured in volts (V)
  • Pushes current through circuits
  • Calculated as \( V = I \cdot R \)

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