Final answer:
a) The value of R that will cause 4 A of current to flow through the 80Ω resistor is 30Ω. b) The power dissipated by the resistor R is 1280W. c) The power generated by the current source is 480W.
Step-by-step explanation:
a) Find the value of R that will cause 4 A of current to flow through the 80Ω resistor in the circuit shown.
To find the value of R, we can use Ohm's Law. Ohm's Law states that the current (I) flowing through a resistor is equal to the voltage (V) across the resistor divided by the resistance (R). In this case, the current is 4 A and the resistance is 80Ω. So, we can rearrange the equation to solve for R: R = V/I = 80Ω.
b) How much power will the resistor R from part (a) need to dissipate?
To find the power dissipated by the resistor, we can use the formula P = IV, where P is power, I is current, and V is voltage. In this case, the current is 4 A and the voltage across the resistor can be found using Ohm's Law: V = IR = 4A * 80Ω = 320V. So, the power dissipated by the resistor is P = IV = 4A * 320V = 1280W.
c) How much power will the current source generate for the value of R from part (a)?
Since the current source is supplying the same current (4A) regardless of the value of R, the power generated by the current source will be the product of the current and the voltage across it. The voltage across the current source can be found using Ohm's Law: V = IR = 4A * 30Ω = 120V. So, the power generated by the current source is P = IV = 4A * 120V = 480W.