Multiple Choice
What is the voltage of the battery below?
27. Resistors & DC Circuits
Solving Resistor Circuits
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What is current and voltage across each resistor below?
A
V2Ω=5.0 V, i2Ω=4.44 A;
V1Ω=5.0 V, i1Ω=2.22 A;
V3Ω=5.0 V, i3Ω=6.67 A
V1Ω=5.0 V, i1Ω=2.22 A;
V3Ω=5.0 V, i3Ω=6.67 A
B
V2Ω=6.67 V, i2Ω=0.500 A;
V1Ω=3.33 V, i1Ω=0.500 A;
V3Ω=10.0 V, i3Ω=2.23 A
V1Ω=3.33 V, i1Ω=0.500 A;
V3Ω=10.0 V, i3Ω=2.23 A
C
V2Ω= 1.82V, i2Ω=0.908 A;
V1Ω=1.82 V, i1Ω=0.908 A;
V3Ω=8.18 V, i3Ω=1.36 A
V1Ω=1.82 V, i1Ω=0.908 A;
V3Ω=8.18 V, i3Ω=1.36 A
D
V2Ω=6.67 V, i2Ω=3.33 A;
V1Ω=3.33 V, i1Ω=3.33 A;
V3Ω=10.0 V, i3Ω=3.33 A
V1Ω=3.33 V, i1Ω=3.33 A;
V3Ω=10.0 V, i3Ω=3.33 A
Verified step by step guidance1
Identify the type of circuit: The circuit consists of a parallel combination of a 2Ω and a 1Ω resistor, which is in series with a 3Ω resistor.
Calculate the equivalent resistance of the parallel resistors: Use the formula for parallel resistance, \( \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} \), where \( R_1 = 2Ω \) and \( R_2 = 1Ω \).
Add the equivalent resistance of the parallel combination to the series resistor: The total resistance \( R_{total} = R_{eq} + 3Ω \).
Use Ohm's Law to find the total current in the circuit: \( I = \frac{V}{R_{total}} \), where \( V = 10V \).
Determine the voltage across each resistor: For the parallel resistors, the voltage is the same and equals the total voltage minus the voltage across the 3Ω resistor. Use Ohm's Law \( V = IR \) to find the voltage across the 3Ω resistor and then the current through each parallel resistor using \( I = \frac{V}{R} \).
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