Question

An automobile battery, when connected to a car radio, provides 12.5 V to the radio. When connected to a set of headlights, it provides 11.7 V to the headlights. Assume the radio can be modeled as a 7.9Ω resistor and the headlights can be modeled as a 0.65Ω resistor. What is the Thevenin equivalent voltage for the battery?

Answer 1

The Thevenin equivalent voltage for the battery is 0.8 V.

Step-by-step explanation:

The Thevenin equivalent voltage of the battery is the voltage across the terminals of the battery with no load connected. When the car radio, modeled as a 7.9Ω resistor, is connected to the battery, the voltage drop across the radio is 12.5 V. When the headlights, modeled as a 0.65Ω resistor, are connected to the battery, the voltage drop across the headlights is 11.7 V.

To find the Thevenin equivalent voltage, we need to find the open circuit voltage, which is the voltage when no load is connected. Since both the radio and headlights cause a voltage drop, we can subtract the voltage drops from the battery voltage. The Thevenin equivalent voltage is therefore:

Thevenin voltage = Battery voltage - Voltage drop across radio - Voltage drop across headlights

Thevenin voltage = 12.5 V - 11.7 V = 0.8 V