Question

Three resistors 10 ohms, 20 ohms, and 30 ohms are connected in series with a 90-volt battery.  Determine the current through each resistor.  Which of the three resistors is the most powerful?

Answer 1

Since the resistors are in series, the equivalent resistance is the sum of the resistances:

$\begin{gathered} R=10+20+30 \\ R=60\text{ ohms} \end{gathered}$

Now, to find the current, let's divide the voltage by the total resistance:

$\begin{gathered} I=\frac{V}{R} \\ I=\frac{90}{60} \\ I=1.5\text{ A} \end{gathered}$

The current through each resistor is the same because they are in series: 1.5 A.

To find the most powerful resistor, let's analyze the formula for the power in a resistor:

$P=I^2\cdot R$

We can see that the greater the resistance, the greater the power, therefore the most powerful resistor is the 30 ohms resistor.