Overview
This lecture covers the voltage divider circuit, methods to calculate voltages and currents in such circuits, design considerations, and efficiency implications when connecting external devices.
Voltage Divider Circuit Basics
- A voltage divider consists of two resistors in series with a voltage source.
- Total resistance in series: ( R_{total} = R_1 + R_2 ).
- Current in the circuit: ( I = \frac{V_{battery}}{R_{total}} ).
- Voltage across ( R_2 ): ( V_{R2} = I \times R_2 ).
- Output voltage formula: ( V_{out} = V_{battery} \times \frac{R_2}{R_1 + R_2} ).
Design Examples
- For a 12V battery, desired 6V output, and 60mA current: set ( R_1 = R_2 = 100\Omega ).
- For 20V battery, 12V output, and 50mA current: total resistance 400Ω; solve ( V_{out} = V_{in} \times \frac{R_2}{R_1+R_2} ) to get ( R_2 = 240\Omega ), ( R_1 = 160\Omega ).
Impact of Connected Devices
- Connecting a device (load) in parallel with ( R_2 ) reduces the output voltage.
- Equivalent resistance for ( R_2 ) and device: ( R_{eq} = \left(\frac{1}{R_2} + \frac{1}{R_{load}}\right)^{-1} ).
- The lower the device resistance, the more voltage drops across ( R_2 ).
- To minimize voltage drop, device resistance should be much greater than ( R_2 ) (ideally 100×).
Efficiency Considerations
- If ( R_2 ) is much less than device resistance, most energy is lost in ( R_2 ) and not used by the device.
- For high efficiency, remove ( R_2 ) and use only the device as ( R_2 ).
- In ideal design, all current flows through the device, maximizing efficiency.
Key Terms & Definitions
- Voltage Divider — A circuit that splits input voltage into a reduced output voltage using two series resistors.
- Equivalent Resistance — Combined resistance of parallel resistors: ( R_{eq} = \left(\frac{1}{R_1} + \frac{1}{R_2}\right)^{-1} ).
- Load — An external device connected across a voltage divider._
Action Items / Next Steps
- Practice designing voltage divider circuits for specific output voltages and currents.
- Calculate efficiency when connecting loads of various resistances.
- Read about practical applications and limitations of voltage divider circuits.