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 6.4? resistor and the headlights can be modeled as a 0.55? resistor.Part A - vth = 12.6VPart BWhat is the Thevenin equivalent resistance for the battery?Part CWhat is the Norton equivalent current for the battery?Part DWhat is the Norton equivalent resistance for the battery?

Answer 1

To determine the Thevenin and Norton equivalents of the battery's internal resistance, currents for both the radio and headlights must be calculated, and the voltage drop must be used to find the battery's internal resistance. Once known, this resistance is the basis for both the Thevenin equivalent resistance and the Norton equivalent resistance, with the Norton current calculated through Ohm's Law with the Thevenin voltage.

Step-by-step explanation:

To determine the Thevenin equivalent resistance of an automobile battery when connected to both a car radio and headlights, we need to observe how the voltage of the battery changes under different loads. Given that the voltage drops from 12.5 V (on the radio) to 11.7 V (on the headlights), and considering the given resistances for the radio and the headlights (6.4Ω and 0.55Ω respectively), we can solve for the internal resistance (r) of the battery using the voltage drop.

First, calculate the currents using Ohm's Law (I = V/R) when the battery is connected to each of the devices:

• Current for the radio: I = 12.5V / 6.4Ω = 1.953 A
• Current for the headlights: I = 11.7V / 0.55Ω = 21.273 A

Now using the voltage drop (ΔV = IR) to find the internal resistance of the battery:

12.5V (no load) - 12.5V (radio) = 1.953 A * r

12.5V (no load) - 11.7V (headlights) = 21.273 A * r

Solving for r gives us the Thevenin equivalent resistance. Both equations should yield the same value for r, taking into account any measurement or rounding errors. Once r is known, the Norton equivalent current can be found using the Thevenin voltage (Vth) and the equivalent resistance (r) by applying Ohm's Law in the form I = Vth/r. The Norton equivalent resistance is the same as the Thevenin equivalent resistance.

Answer 2

Base on the question, and in my further computation, the possible answers would be the following and I hope you are satisfied with my answer and feel free to ask for more.

- If you want to determine the Thevenin equivalent voltage and resistance without overloading the battery, then apply some known resistance

RLRL and measure the output voltage as VLVL. Measure the voltage without a load as VOCVOC. The voltage divider equation tells us that

VL=VOCRLRTH×RLVL=VOCRLRTH×RL

Solve for RTHRTH, and you know that VTH=VOCVTH=VOC.