Electric Circuits
Intermediate
Ohm's Law
Source: High school physics (Chinese)
Problem Sets:
ohm's law
Problem
Two resistors are given. When they are connected in parallel, the total resistance is $2.4 \ \Omega$. When they are connected in series, the total resistance is $10 \ \Omega$.
What are the resistance values of the two resistors?
$R_1 = 4 \ \Omega$, $R_2 = 6 \ \Omega$.
Let the two resistances be $R_1$ and $R_2$.
Series: $R_1 + R_2 = 10 \ \Omega$.
Parallel: $\dfrac{R_1 R_2}{R_1 + R_2} = 2.4 \ \Omega$, so $R_1 R_2 = 2.4 \times 10 = 24 \ \Omega^2$.
$R_1$ and $R_2$ are the roots of $x^2 - 10x + 24 = 0$, i.e. $(x-4)(x-6)=0$.