calculate the resistances of (a) 100-watt 120-volt incandescent lamp, (b) a 750-watt 115-volt toaster, (c) a 1300 watt 110-volt portable iron.

A 72-ohm coil of wire is connected in series with an adjustable resistor (rheostat) whose resistance can be varied from 0 to 88 ohms. If the line potential is 115 volts, calculate (a) the range through which the coil current can be varied, (b) the rheostat resistance when the power taken by the coil is 90 watts

a. 120I = 100 W.

I = 0.833A

R = V/I = 120/0.833 = 144 Ohms.

b. Same procedure as a.

c. Same procedure as a.

a. Imax = V/(72+0) = 115/(72+0) = 1.60A
Imin = 115/(72+88) = 0.719A

b. P = V^2/(Rc+R) = 90 W.
115^2/(72+R) = 90
90*(72+R) = 115^2
72+R = 146.94
R = 146.94-72 = 74.94 Ohms=The rheostat
resistance.

Well, let's shed some light on these resistances, shall we?

(a) 100-watt 120-volt incandescent lamp:
To calculate the resistance, we'll use Ohm's Law, which states that resistance (R) equals voltage (V) divided by current (I). The power (P) of the lamp is 100 watts, and the voltage (V) is 120 volts. We can find the current (I) using P = VI. So, I = P/V = 100/120 ≈ 0.833 amps. Now we can calculate the resistance using R = V/I = 120/0.833 ≈ 144 ohms.

(b) 750-watt 115-volt toaster:
Again, using Ohm's Law, we need to find the current (I). P = VI, so I = P/V = 750/115 ≈ 6.52 amps. Now we can calculate the resistance using R = V/I = 115/6.52 ≈ 17.6 ohms.

(c) 1300-watt 110-volt portable iron:
One more time with Ohm's Law! I = P/V = 1300/110 ≈ 11.82 amps. Finally, R = V/I = 110/11.82 ≈ 9.31 ohms.

So, the resistances are approximately:
(a) 144 ohms
(b) 17.6 ohms
(c) 9.31 ohms

Keep in mind that these are approximate values, so don't expect the resistances to toast you some accurate bread!

To calculate the resistances of these devices, we can use Ohm's Law, which states that resistance (R) is equal to voltage (V) squared divided by power (P).

(a) For the 100-watt 120-volt incandescent lamp:
Resistance (R) = V^2 / P = (120^2) / 100 = 144Ω

(b) For the 750-watt 115-volt toaster:
Resistance (R) = V^2 / P = (115^2) / 750 = 17.733Ω

(c) For the 1300-watt 110-volt portable iron:
Resistance (R) = V^2 / P = (110^2) / 1300 = 9.351Ω

Therefore, the resistances of the devices are:
(a) 144Ω
(b) 17.733Ω
(c) 9.351Ω

To calculate the resistances of each device, we can use Ohm's law, which states that the resistance (R) of an electrical device is equal to the voltage (V) squared divided by the power (P) consumed by the device.

(a) To calculate the resistance of the 100-watt 120-volt incandescent lamp, we can use the formula:

R = V^2/P

R = (120^2)/100

R = 14400/100

R = 144 ohms

Therefore, the resistance of the 100-watt 120-volt incandescent lamp is 144 ohms.

(b) To calculate the resistance of the 750-watt 115-volt toaster:

R = V^2/P

R = (115^2)/750

R = 13225/750

R = 17.67 ohms

Therefore, the resistance of the 750-watt 115-volt toaster is approximately 17.67 ohms.

(c) To calculate the resistance of the 1300-watt 110-volt portable iron:

R = V^2/P

R = (110^2)/1300

R = 12100/1300

R = 9.31 ohms

Therefore, the resistance of the 1300-watt 110-volt portable iron is approximately 9.31 ohms.