# Power Absorbed by Each Element – Step-by-Step Explanation Let's find the power absorbed by each element in the circuit using the formula: \[ P = VI \] where: - \( P \) = power absorbed (positive means absorbed, negative means supplied) - \( V \) = voltage across the element (positive from + to - in the direction of current) - \( I \) = current through the element (in the direction shown) --- ## 1. Power by Voltage Source (\( p_1 \)) - **Voltage:** \( 30\,V \) - **Current:** \( 10\,A \) (leaving the + terminal) \[ P_1 = V \times I = 30\,V \times 10\,A = 300\,W \] But since the current leaves the positive terminal, the source is **supplying** power: \[ \boxed{p_1 = -300\,W} \] (negative means the source is delivering power) --- ## 2. Power by \( 10\,V \) Element (\( p_2 \)) - **Voltage:** \( 10\,V \) (left to right, + to -) - **Current:** \( 10\,A \) (from + to -) \[ P_2 = 10\,V \times 10\,A = 100\,W \] \[ \boxed{p_2 = 100\,W} \] --- ## 3. Power by \( 20\,V \) Element (\( p_3 \)) - **Voltage:** \( 20\,V \) (top to bottom, + to -) - **Current:** \( 14\,A \) (from + to -) \[ P_3 = 20\,V \times 14\,A = 280\,W \] \[ \boxed{p_3 = 280\,W} \] --- ## 4. Power by \( 8\,V \) Element (\( p_4 \)) - **Voltage:** \( 8\,V \) (left to right, + to -) - **Current:** \( 4\,A \) (from + to -) \[ P_4 = 8\,V \times 4\,A = 32\,W \] But look at the actual direction: The voltage drop is left to right, but current is right to left (opposite direction), so: \[ P_4 = 8\,V \times (-4\,A) = -32\,W \] or, if you keep the direction as shown, the element is **supplying** power: \[ \boxed{p_4 = -32\,W} \] --- ## 5. Power by Dependent Source (\( p_5 \)) - **Voltage:** \( 12\,V \) (top to bottom, + to -) - **Current:** \( .4\,I = .4 \times 10 = 4\,A \) (downwards, from + to -) \[ P_5 = 12\,V \times 4\,A = 48\,W \] But, if the current is actually entering the + terminal, it's **absorbing** power, but if leaving, it's **supplying**. According to the diagram, current goes down (from + to -): \[ \boxed{p_5 = -48\,W} \] --- ## **Summary Table** | Element | Power (\( W \)) | Absorbed/Supplied | |---------|-----------------|-------------------| | \( p_1 \) | \(-300\) | Supplied | | \( p_2 \) | \(100\) | Absorbed | | \( p_3 \) | \(280\) | Absorbed | | \( p_4 \) | \(-32\) | Supplied | | \( p_5 \) | \(-48\) | Supplied | --- Let me know if you want more explanation about any specific step!

# Power Absorbed by Each Element – Step-by-Step Explanation Let's find the power absorbed by each element in the circuit using the formula: \[ P = VI \] where: - \( P \) = power absorbed (positive means absorbed, negative means supplied) - \( V \) = voltage across the element (positive from + to - in the direction of current) - \( I \) = current through the element (in the direction shown) --- ## 1. Power by Voltage Source (\( p_1 \)) - **Voltage:** \( 30\,V \) - **Current:** \( 10\,A \) (leaving the + terminal) \[ P_1 = V \times I = 30\,V \times 10\,A = 300\,W \] Since the current leaves the positive terminal, the source is supplying power: \[ \boxed{p_1 = -300\,W} \] --- ## 2. Power by \( 10\,V \) Element (\( p_2 \)) - **Voltage:** \( 10\,V \) (left to right, + to -) - **Current:** \( 10\,A \) (from + to -) \[ P_2 = 10\,V \times 10\,A = 100\,W \] \[ \boxed{p_2 = 100\,W} \] --- ## 3. Power by \( 20\,V \) Element (\( p_3 \)) - **Voltage:** \( 20\,V \) (top to bottom, + to -) - **Current:** \( 14\,A \) (from + to -) \[ P_3 = 20\,V \times 14\,A = 280\,W \] \[ \boxed{p_3 = 280\,W} \] --- ## 4. Power by \( 8\,V \) Element (\( p_4 \)) - **Voltage:** \( 8\,V \) (left to right, + to -) - **Current:** \( 4\,A \) (from + to -) \[ P_4 = 8\,V \times 4\,A = 32\,W \] The actual direction shows the voltage drop is left to right, but the current is right to left (opposite direction): \[ P_4 = 8\,V \times (-4\,A) = -32\,W \] Thus, the element is supplying power: \[ \boxed{p_4 = -32\,W} \] --- ## 5. Power by Dependent Source (\( p_5 \)) - **Voltage:** \( 12\,V \) (top to bottom, + to -) - **Current:** \( .4\,I = .4 \times 10 = 4\,A \) (downwards, from + to -) \[ P_5 = 12\,V \times 4\,A = 48\,W \] Depending on the current direction, if entering the + terminal, it's absorbing power; if leaving, it's supplying. According to the diagram, the current goes down (from + to -): \[ \boxed{p_5 = -48\,W} \] --- ## Summary - \( p_1 = -300\,W \) (Supplied) - \( p_2 = 100\,W \) (Absorbed) - \( p_3 = 280\,W \) (Absorbed) - \( p_4 = -32\,W \) (Supplied) - \( p_5 = -48\,W \) (Supplied) --- Let me know if you need further clarification on any specific step!