Learning Goal: To practice Problem-Solving Strategy 23.1 Resistor Circuits. Find the currents through and the potential…
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Question “Learning Goal: To practice Problem-Solving Strategy 23.1 Resistor Circuits. Find the currents through and the potential…”
Learning Goal:
To practice Problem-Solving Strategy 23.1 Resistor Circuits.
Find the currents through and the potential difference across
each resistor in the circuit shown on the diagram (Figure 1) . Use
the following values: E = 12.0V , R1 = 15.0? , R2
= 45.0? , R3 = 20.0? , and R4 = 25.0? .
PROBLEM-SOLVING STRATEGY 23.1 Resistor Circuits
We can analyze any resistor circuit by sequentially reducing
parallel and series resistor combinations to their equivalent
resistors until only the battery and a single equivalent resistor
are left.
PREPARE Draw a circuit diagram. Label all known
and unknown quantities.
SOLVE Base your mathematical analysis on
Kirchhoff’s laws and on the rules for series and parallel
resistors.
Step by step, reduce the circuit to the smallest possible number
of equivalent resistors.
Determine the current through and potential difference across
the equivalent resistors.
Rebuild the circuit, using the facts that the current is the
same through all resistors in series and the potential difference
is the same for all parallel resistors.
ASSESS Use two important checks as you rebuild
the circuit:
Verify that the sum of the potential differences across series
resistors matches ?V for the equivalent resistor.
Verify that the sum of the currents through parallel resistors
matches I for the equivalent resistor.
Prepare
The circuit drawing is already given in the problem
introduction. The battery voltage and all resistances are known.
The current through and voltage across each resistor are
unknown.
Solve
Use the information and the insights that you have accumulated
to construct the necessary mathematical expressions and to derive
the solution. You will need to solve parts C and D together.
Part A
Step by step, reduce the circuit to the smallest possible number
of equivalent resistors in order to find the equivalent resistance
Req of the entire circuit.
Express you answer in ohms to three significant figures.
Req= | ? |
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Part
Part B
Find Ieq, the current through the equivalent
resistor.
Express your answer in amperes to three significant figures.
Ieq= | A |
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Part
Follow up to come
SHOW ALL WORK PLEASE *******
Answer
R3+R4 = 45 =r 1/(1/r+(1/45)), = 45/2 = 22.5 =r’
Requi = 22.5+15 = 37.5
I = 12/37.5 = 0.32A
I1 = 0.32A, V1 = I1R1 = 4.8V
I2 = 0.32/2 = 0.16A, V2 = I2R2 = 7.2V
I3 = 0.32/2 = 0.16A, V3 = I3R3 = 3.2V
I4 = 0.32/2 = 0.16A, V4 = I4R4 = 4.0V
Conclusion
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