What is the value of V0 in the given circuit diagram?
Understand the Problem
The question is asking us to analyze the given electrical circuit and likely calculate the voltage (V0) across one of the resistors, considering the voltage sources and the resistances present in the circuit.
Answer
The voltage \( V_0 \) across the \( 1 \, \Omega \) resistor is \( V_0 = 3.2 \, V \).
Answer for screen readers
The voltage ( V_0 ) across the ( 1 , \Omega ) resistor is ( V_0 = 3.2 , V ).
Steps to Solve

Identify the components We have resistors of ( 4 , \Omega ), ( 1 , \Omega ), ( 3 , \Omega ), and ( 5 , \Omega ) as well as two voltage sources of ( 9V ) and ( 3V ).

Determine total resistance The ( 4 , \Omega ) and ( 1 , \Omega ) resistors are in series. Their equivalent resistance ( R_1 ) is calculated as: $$ R_1 = 4 , \Omega + 1 , \Omega = 5 , \Omega $$

Combine resistances in parallel Now the ( R_1 ) equivalent resistance (( 5 , \Omega )) is in parallel with the ( 3 , \Omega ) resistor. The total resistance ( R_{total} ) can be calculated using the formula for parallel resistors: $$ \frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{3 , \Omega} $$ $$ \frac{1}{R_{total}} = \frac{1}{5} + \frac{1}{3} = \frac{3 + 5}{15} = \frac{8}{15} $$ Thus, $$ R_{total} = \frac{15}{8} , \Omega $$

Find the voltage in the circuit Next, apply the voltage sources. The effective voltage ( V_{source} ) in the loop is: $$ V_{source} = 9 , V  3 , V = 6 , V $$

Calculate the total current Using Ohm’s Law, we can find the total current ( I ) flowing through the circuit: $$ I = \frac{V_{source}}{R_{total}} = \frac{6 , V}{\frac{15}{8} , \Omega} = \frac{6 \times 8}{15} = \frac{48}{15} = 3.2 , A $$

Determine voltage across resistors To find ( V_0 ) across the ( 1 , \Omega ) resistor, apply Ohm’s Law: $$ V_0 = I \cdot R = 3.2 , A \cdot 1 , \Omega = 3.2 , V $$
The voltage ( V_0 ) across the ( 1 , \Omega ) resistor is ( V_0 = 3.2 , V ).
More Information
This circuit analysis involves using basic principles of series and parallel resistances, combined with Ohm’s Law and voltage source effects. Understanding these concepts is key to electrical circuit analysis.
Tips
 Failing to correctly apply the series and parallel rules for resistances.
 Confusing the direction or signs of voltage sources when calculating net voltage.
 Not properly using Ohm's Law might lead to incorrect current and voltage values.