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Electrical Circuits: Resistors and Power

A 15 V battery is connected with a 5 Ω resistor and a 10 Ω resistor in series. Find the power from the 5 Ω resistor.

$Ohm's\ Law:\ V=I\cdot R$

$Kirchoff's\ 2^{nd}\ Law:\ All\ voltages\ must\ add\ to\ 0\ in\ a\ loop.$

For a series circuit:

- The current is the same throughout the circuit
- The equivalent resistance is the sum of the resistors

$R_{eq}=5\Omega +10\Omega =15\Omega,\ V=I\cdot R,\ I=\frac{V}{R}=\frac{15\ V}{15\ \Omega}=1\ A$

$P=I\cdot V$

$P=I\cdot (I\cdot R)$

$P=I^{2}\cdot R$

$P=(1\ A)^{2}(5\ \Omega)=5\ W$

Now consider the same circuit but with two resistors in a parallel circuit. Find the power from the 5 Ω resistor.

$Use\ Kirchoff's\ 2^{nd}\ Law\ to\ find\ voltage\ of\ 5\ \Omega$

$V=I\cdot R,\ I=\frac{V}{R}=\frac{15\ V}{5\ \Omega}=3\ A$

$P=I\cdot V=(3\ A)(15\ V)=45\ W$

For a parallel circuit:

- The current is not the same throughout the circuit
- $\frac{1}{R_{G}}=\frac{1}{R_{1}} +\frac{1}{R_{2}} +\ ...$