Question

A radio and a variable resistor are connected in series with a 15 V source.The radio has a resistance value of 60 22. The total current needed in thecircuit is 0.2 amps in order for the radio to work. What is the value of thevariable resistor necessary?

Answer 1

We are given a series circuit with two resistors and a voltage source. Since the resistor are in series this means that the total resistance is the sum of both resistances. Applying Ohm's law we get

$V=I(R_1+R_2)$

Where:

V is voltage, I is current and R1 and R2 are the resistance of the radio and the variable resistance respectively.

Now we solve for the variable resistance, R2, first by dividing both sides by I:

$\frac{V}{I}=R_1+R_2$

Now we subtract R1 to both sides:

$\frac{V}{I}-R_1=R_2_{}$

Replacing the values:

$\frac{15V}{0.2A}+60O\text{hm}=R_2$

Solving the operations:

$\begin{gathered} 75Ohm+60Ohm=R_2 \\ 135Ohm=R_2 \end{gathered}$

Therefore, the resistance needed is 135 Ohms.