Questions: Given: R1=30 Ω, R2=28 Ω, Vo=84 V, I=3 A, calculate the node voltage, V1.

Transcript text: Given: $\mathrm{R} 1=30 \Omega, \mathrm{R} 2=28 \Omega, \mathrm{Vo}=84 \mathrm{~V}, \mathrm{I}=3 \mathrm{~A}$, calculate the node voltage, $\mathrm{V}_{1}$. $\square$ Not saved Submit

Solution

Solution Steps

Step 1: Identify the Circuit Configuration

Given the resistances $ R_1 = 30 \, \Omega $, $ R_2 = 28 \, \Omega $, the output voltage $ V_o = 84 \, \text{V} $, and the current $ I = 3 \, \text{A} $, we need to determine the node voltage $ V_1 $.

Step 2: Apply Ohm's Law to Find Voltage Drops

Using Ohm's Law, $ V = IR $, we can find the voltage drops across each resistor.

For $ R_1 $: \[ V_{R1} = I \cdot R_1 = 3 \, \text{A} \cdot 30 \, \Omega = 90 \, \text{V} \]

For $ R_2 $: \[ V_{R2} = I \cdot R_2 = 3 \, \text{A} \cdot 28 \, \Omega = 84 \, \text{V} \]

Step 3: Determine the Node Voltage $ V_1 $

The node voltage $ V_1 $ is the voltage at the node between $ R_1 $ and $ R_2 $. Since $ V_o $ is given as 84 V and $ V_{R2} $ is also 84 V, the voltage at the node $ V_1 $ must be the same as $ V_{R2} $.

\[ V_1 = V_{R2} = 84 \, \text{V} \]