Q5. - Algebra 2

Question

Find the amount of current I (in amperes) produced if the electromotive force E is 2.5 volts, the circuit resistance R is 1.05 ohms, and the resistance r within a battery is 0.2 ohm. Use the formula $I=\frac{E}{R+r}$

Step-by-Step Solution

Answer

Amount of current produced is 2 amperes

Step 1 - Order for simplification

To evaluate any expression involving more than one operation, follow the below order of operations:

• First evaluate expressions inside grouping symbols like parentheses ( ) or brackets [ ].
• Evaluate the exponents.
• Perform Multiplication and division from left to right.
• Perform addition and subtraction from left to right.

Step 2 - Substitution

Substitute 2.5 for E, 1.05 for R, and 0.2 for r in given expression.

$\begin{array}{c}I=\frac{E}{R+r}\\ =\frac{2.5}{1.05+0.2}\end{array}$

Step 3 - Simplify expression of denominator

To evaluate the value of the given expression, first simplify denominator as shown below]

$\begin{array}{c}I=\frac{2.5}{1.05+0.2}\\ =\frac{2.5}{1.25}\end{array}$

Step 4 - Divide 2.5 with 1.25

Now, to simplify further divide the numbers to get, 

$\begin{array}{c}I=\frac{2.5}{1.25}\\ =2\end{array}$

The unit of current is amperes. Thus $I = 2 amperes$