series connection
no junction → same current passes through each resistors
$$I_{1}=I_{2}=I_{3}=I$$
$$\underbrace{ V_{1}=V_{2}=V_{3} }{ \text{energy taken up by resistors} } =\underbrace{ \epsilon }{ \text{energy delivered by emf source} } $$
Energy taken up by resistors
$$I \cdot R_{1}+I \cdot R_{2}+I \cdot R_{3}$$
$$V_{1}:V_{2}:V_{3}=R_{1}:R_{2}:R_{3}$$
# Equivalent resistance of resistors in a series
equivalent resistance is equal to the sum of resistances
$\epsilon=I \cdot R_{1}+I \cdot R_{2}+I \cdot R_{3}$ $\epsilon=I \cdot R_{e}$
Chrismas lights
line of 50 chrismas lights
$I=2\text{ A}$
$V=230\text{ V}$
$R_{\text{ one light}}=?$
$$R=\frac{V}{I}$$
$$R_{\text{ one}}=\frac{R}{50}$$
$$R_{\text{ one}}=2.3 \Omega$$
# Applications
- chrismas lights
- fuse