Problem 27 - Elementary Algebra

Question

Use numerical evaluation to evaluate the equations for the following problems. $$ I=\frac{E}{R} . \quad \text { Find } I \text { if } E=20 \text { and } R=2 . $$

Step-by-Step Solution

Answer

Question: Calculate the current (I) when the voltage (E) is 20 volts and resistance (R) is 2 ohms. Answer: The current (I) is 10 amperes.

Step 1: Write down the formula

The formula to calculate the current (I) is given by: $$ I=\frac{E}{R} $$

Step 2: Plug in given values

We are given the values for E and R. Plug these values into the formula: $$ I=\frac{20}{2} $$

Step 3: Evaluate the equation

Now, evaluate the expression: $$ I= \frac{20}{2} = 10 $$

Step 4: State the final answer

The current (I) when E = 20 and R = 2 is 10 amperes.

Key Concepts

Understanding Current Calculation

In electrical circuits, the current calculation is essential for determining the flow of electric charge. Current, denoted as \( I \), indicates how much charge flows through a point in the circuit per unit of time. To calculate it, we often use Ohm’s Law, which provides the relationship between current, voltage (or electromotive force \( E \)), and resistance \( R \). The formula is straightforward: \( I = \frac{E}{R} \).

This equation allows us to find the current by dividing the voltage by the resistance. It is crucial in designing and analyzing electrical systems, ensuring they function correctly and safely.

• Voltage \( E \) is the potential difference in charge between two points.
• Resistance \( R \) opposes the flow of current, measured in ohms.
• Current \( I \) is measured in amperes (amps).

Using these basic concepts, electrical engineers can solve various problems and design circuits that meet specific requirements. In the given problem, when \( E = 20 \) volts and \( R = 2 \) ohms, the current \( I \) is calculated to be 10 amperes.

Executing Equation Evaluation

Equation evaluation is the process of substituting known values into an equation to find the unknown variables. This task involves both algebraic manipulation and computational skills, allowing us to predict or confirm the behavior of a system.

In our specific exercise, after identifying the given formula \( I = \frac{E}{R} \), we substitute the values \( E = 20 \) and \( R = 2 \) into the equation. This substitution transforms the abstract formula into a form that can be computed:

• Substitute \( E \) into the equation: \( I = \frac{20}{R} \)
• Substitute \( R \) into the equation: \( I = \frac{20}{2} \)

Equation evaluation is a fundamental math skill used in numerous fields such as physics, engineering, and economics. It forms the basis of modeling real-world situations mathematically, deriving insights, and making computations easier.

Exploring Division in Algebra

Division is one of the core operations in algebra and involves splitting a quantity into equal parts. In algebraic equations, it's used to solve for unknowns by isolating variables to find their values.

For example, when evaluating the expression \( I = \frac{20}{2} \), we perform the division to compute the current \( I \):

• Determine how many times 2 fits into 20, which results in 10.
• The division solves for \( I \), giving the value 10 amps.

This concept is not limited to numbers; it extends to variables and expressions. Division helps to simplify complex equations and break them into manageable parts.

Understanding how to properly divide within an equation allows you to systematically find solutions in algebraic problems, making this operation a vital tool in mathematical problem-solving.