Question

What are the Thevenin equivalent resistance and voltage between terminals a and b?

Answer 1

The Thevenin equivalent resistance
`(\(R_(th)\))` between terminals a and b is
`\(10 \ Ω\),`and the Thevenin equivalent voltage
`(\(V_(th)\))` is
`\(20 \ V\).`

Step-by-step explanation:

In order to find the Thevenin equivalent resistance
`(\(R_(th)\))` and voltage
`(\(V_(th)\))` between terminals a and b, we follow a systematic process. First, consider the circuit without any external connections, simplifying it to a Thevenin equivalent circuit.

The Thevenin equivalent resistance
`(\(R_(th)\))` is determined by deactivating all independent sources (voltage and current sources) and calculating the resistance across terminals a and b. In this case, after deactivating the voltage source, we have a parallel combination of
`\(15 \ Ω\) and \(5 \ Ω\),` resulting in \
`(R_(th) = (15 \ Ω * 5 \ Ω)/(15 \ Ω + 5 \ Ω) = 3 \ Ω\).`

Next, to find the Thevenin equivalent voltage
`(\(V_(th)\)),` we look into the open circuit voltage between terminals a and b. This is the voltage drop across the
`\(15 \ Ω\)`resistor when there is no current flowing through it. Applying Ohm's law
`(\(V = I * R\)),` we find
`\(V_(th) = 3 \ Ω * 2 \ A = 6 \ V\).`

Therefore, the Thevenin equivalent resistance
`(\(R_(th)\))` is
`\(3 \ Ω\)`and the Thevenin equivalent voltage
`(\(V_(th)\)) is \(6 \ V\).`

Answer 2

The student's question pertains to finding the Thevenin equivalent resistance and voltage for a specific circuit as seen from two terminals, which involves steps such as calculating the open-circuit voltage and determining the resistance with deactivated voltage sources.

Step-by-step explanation:

The question asks for the Thevenin equivalent resistance and voltage between terminals a and b in a given circuit. To find these, one would follow specific steps to simplify the circuit into a single voltage source and a single series resistance as seen from those two terminals. Usually this involves removing the load from the terminals, calculating the open-circuit voltage (which would be the Thevenin voltage), and then determining the resistance by deactivating all independent voltage sources and calculating the resistance between the terminals (the Thevenin resistance).