Questions: Determine V0 in the given circuit. Assume A=19 Ω and B=16 Ω.

Transcript text: Determine $V_{0}$ in the given circuit. Assume $A=19 \Omega$ and $B=16 \Omega$.

Solution

Solution Steps

Step 1: Identify the components and given values

Resistor A: $ 19 \, \Omega $
Resistor B: $ 16 \, \Omega $
Voltage source 1: $ 10 \, V $
Voltage source 2: $ 25 \, V $

Step 2: Apply Kirchhoff's Voltage Law (KVL)

Kirchhoff's Voltage Law states that the sum of all voltages around a closed loop must equal zero. For the given circuit, we can write the KVL equation as: \[ 10V - V_A - V_o - V_B + 25V = 0 \]

Step 3: Calculate the voltage drops across resistors A and B

Using Ohm's Law ($ V = IR $), we need to find the current $ I $ in the circuit. The total resistance $ R_{total} $ is the sum of resistances A and B: \[ R_{total} = A + B = 19 \, \Omega + 16 \, \Omega = 35 \, \Omega \]

The total voltage $ V_{total} $ is the sum of the voltage sources: \[ V_{total} = 10V + 25V = 35V \]

The current $ I $ in the circuit is: \[ I = \frac{V_{total}}{R_{total}} = \frac{35V}{35 \, \Omega} = 1A \]

Step 4: Calculate the voltage drops across resistors A and B

\[ V_A = I \times A = 1A \times 19 \, \Omega = 19V \] \[ V_B = I \times B = 1A \times 16 \, \Omega = 16V \]

Step 5: Determine $ V_o $

Using the KVL equation: \[ 10V - 19V - V_o - 16V + 25V = 0 \] \[ 10V + 25V - 19V - 16V - V_o = 0 \] \[ 35V - 35V - V_o = 0 \] \[ -V_o = 0 \] \[ V_o = 0V \]

Final Answer

\[ V_o = 0V \]

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