Given the formula [tex]$E=I R$[/tex], what is the formula for [tex]$R$[/tex]?
A. [tex]$R=I E$[/tex]
B. [tex]$R=I \div E$[/tex]
C. [tex]$R=E I$[/tex]
D. [tex]$R=E+I$[/tex]
Answer (2)
Start with the formula E = I R .
Divide both sides by I to isolate R : I E โ = I I R โ .
Simplify to find the formula for R : R = I E โ .
The formula for R is R = I E โ โ .
Explanation
Understanding the Problem We are given the formula E = I R and asked to find the formula for R . This involves isolating R on one side of the equation.
Isolating R To isolate R , we need to divide both sides of the equation E = I R by I . This gives us I E โ = I I R โ .
Final Formula Simplifying the right side of the equation, we have I I R โ = R . Therefore, the formula for R is R = I E โ .
Comparing with Options Comparing our result R = I E โ with the given options: A. R = I E B. R = I d i v E C. R = E I D. R = E + I We see that option B, R = I d i v E is equivalent to R = E I โ , which is not the same as our result. However, none of the options match our derived formula exactly. Let's re-examine the step where we isolated R. We have E = I R . Dividing both sides by I, we get I E โ = R . Thus, R = I E โ . Option B is R = I รท E = E I โ , which is incorrect. However, if we interpret the question as asking which operation correctly isolates R, then we are looking for R = I E โ .
Examples
Ohm's Law, E = I R , is a fundamental concept in electrical circuits. If you have a circuit with a voltage source ( E ) and a known current ( I ), you can use this formula to calculate the resistance ( R ) of the circuit. For example, if a circuit has a voltage of 12V and a current of 2A, the resistance is R = 2 A 12 V โ = 6ฮฉ . This calculation is crucial for designing and troubleshooting electrical systems.
The formula for resistance (R) derived from Ohm's Law, E = I R , is R = I E โ . This means resistance is equal to voltage divided by current. None of the given options match this correct formula.
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