The electric current I in a circuit varies directly as the voltage V. When 21V are applied, the current is 4A. What is the current when 18 volts are applied
To find the current when 18 volts are applied, we can use the concept of direct variation. Direct variation means that one variable is directly proportional to another variable. In this case, the current (I) is directly proportional to the voltage (V).
We can set up a proportion using the given information:
I₁ / V₁ = I₂ / V₂
Where:
I₁ = 4A (current when 21V are applied)
V₁ = 21V (applied voltage when current is 4A)
V₂ = 18V (applied voltage we want to find)
I₂ = ? (current when 18V are applied, which we are trying to find)
Plugging in the values, we get:
4A / 21V = I₂ / 18V
To solve for I₂, we cross-multiply and solve the equation:
4A * 18V = 21V * I₂
72A V = 21V * I₂
Divide both sides by 21V to isolate I₂:
(72A V) / 21V = I₂
Now, simplify the expression:
I₂ = 72A / 21
I₂ ≈ 3.43A
Therefore, the current when 18 volts are applied is approximately 3.43A.
i = k V
4 = k (21)
k = 4/21
i = (4/21) 18 = 4*6/7 = 24/7 = 3.43 amps