parallel resistors

Last updated 2023.03.02 Edit Source

• Physics
• Electricity

each resistor connect to the same two points

$$V_{1}=V_{2}=V_{3}=V_{AB}(=\epsilon)$$
$$\underbrace{ I_{1}+I_{2}+I_{3} }{ \text{charges leaving junction} } =\underbrace{ I }{ \text{charges entering junction} } $$
$$R=\frac{V}{I}\to I=\frac{V}{R}$$
$$I_{1}:I_{2}:I_{3}=\frac{V}{R_{1}}: \frac{V}{R_{2}}: \frac{V}{R_{3}}=\frac{1}{R_{1}}: \frac{1}{R_{2}}: \frac{1}{R_{3}}$$

$$\frac{1}{R_{e}}=\frac{1}{R_{1}}+ \frac{1}{R_{2}}+ \frac{1}{R_{3}}$$

• solar cells
• multi-stage heater
• household electric network

Parallel resistors problem
$$R_{e}=$$