Learning Goal: To practice Problem-Solving Strategy 23.1 Resistor Circuits. Find

Question

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.

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Part B

Find Ieq, the current through the equivalent resistor.

Express your answer in amperes to three significant figures.

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Explanation / 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

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