Question

The figure shows a section of a circuit. The resistances areR₁ = 2.5 Ω, R₂ = 4.4 Ω, andR₃ = 6.6 Ω, and the indicated current isi = 7.9 A. The electric potential difference between points A and B that connect the section to the rest of the circuit is V_A -V_B = 71 V. (a) Is the device represented by “Box” absorbing or providing energy to the circuit, and (b) at what rate?

Answer 1

Solution) R1 = 2.5 ohm

R2 = 4.4 ohm

R3 = 6.6 ohm

i = 7.9 A

VA - VB = 71 V

(a) is the box absorbing or providing energy

From V = iR

V3 = (i)(R3) = (7.9)(6.6) = 52.1 V

i1 = ((VA - VB) - (V3))/(R1)

i1 = ( 71 - 52.1)/(2.5) = 7.56 A

i1 = i + i2

i2 = i1 - i = 7.56 - 7.9 =  - 0.34 A

Power dissipated,

P = (i1^2)(R1) + (i2^2)(R2) + (i^2)(R3)

P = (7.56^2)(2.5) + (0.34^2)(4.4) + (7.9^2)(6.6)

P = 555.3 W

Power supplied

P' = (i1)(VA - VB)

P' = (7.56)(71)

P' = 536.76 W

P > P' so energy is being supplied

So box is supplying additional energy

(b) rate = ?

Rate = P - P'

Rate = 555.3 - 536.76

Rate = 18.54 W