Consider the circuit shown below. 1. Find vo using Kirchoff’s laws and Ohm’s law. 2. Test the solution for vo by verifying that the total power supplied equals the total power abso... Consider the circuit shown below. 1. Find vo using Kirchoff’s laws and Ohm’s law. 2. Test the solution for vo by verifying that the total power supplied equals the total power absorbed.
Understand the Problem
The question is asking to find the voltage vo in a given circuit using Kirchoff's laws and Ohm's law, and then to verify the solution by checking if the total power supplied equals the total power absorbed in the circuit.
Answer
$v_o = V_s - V_{R_1}$ (example formula; replace with actual values according to your circuit)
Answer for screen readers
The correct voltage $v_o$ will be derived from the calculations based on your circuit's components.
In an example circuit: $$ v_o = V_s - V_{R_1} $$
Steps to Solve
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Identify the circuit components Label the components in the circuit, including the resistors, voltage sources, and any current sources. Note their values.
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Apply Kirchhoff's Voltage Law (KVL) Write the KVL equation for the circuit. KVL states that the sum of the electrical potential differences (voltages) around any closed network is zero.
For example, if we have a loop with a voltage source $V_s$ and resistors $R_1$ and $R_2$, the equation will be: $$ V_s - I R_1 - I R_2 = 0 $$
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Rearrange the equation to solve for current Solve the KVL equation for the current $I$. You might rearrange it to get: $$ I = \frac{V_s}{R_1 + R_2} $$
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Calculate the voltage across each resistor Using Ohm's law ($V = I R$), calculate the voltage across each resistor. For example, for resistor $R_1$: $$ V_{R_1} = I \cdot R_1 $$
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Find the voltage at the required point (vo) Determine the voltage $v_o$ at the point of interest in the circuit. This may involve adding or subtracting the voltages you've calculated based on the path you take in the circuit.
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Verify using power calculations Calculate the total power provided by the voltage sources and the power absorbed by the resistors.
The power from the source can be calculated as: $$ P_{\text{source}} = V_s \cdot I $$
The power absorbed by the resistors will be: $$ P_{\text{absorbed}} = V_{R_1} \cdot I + V_{R_2} \cdot I $$
Ensure that: $$ P_{\text{source}} = P_{\text{absorbed}} $$
The correct voltage $v_o$ will be derived from the calculations based on your circuit's components.
In an example circuit: $$ v_o = V_s - V_{R_1} $$
More Information
Understanding how to apply Kirchhoff's laws will help not only in solving this problem but also in analyzing larger and more complex circuits. Verification through power calculations ensures that the circuit obeys the law of conservation of energy.
Tips
- Forgetting to consider the signs of voltages when applying KVL, which can lead to incorrect equations.
- Miscalculating total resistance when resistors are in series or parallel.
- Not verifying the solution using power calculations, which can result in overlooking errors in the voltage calculations.
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