A lamp (R = 151 ), an electric heater (R = 24 ), and a fan (R = 49 ) are connected in parallel across a 121 V line. What total current is supplied to the circuit? What is the voltage across the fan? What is the current in the lamp? What power is expended in the heater?

Il = V/R = 121 v./ 151 ohm = 0.80 A

Ih = 121 / 24 = 5.04 A.
Ph = VI = 121 * 5.04 = 609.8 W.

If = 121 / 47 = 2.47 A.

It = 0.80 + 5.04 + 2.47 = 8.3 A.

To find the total current supplied to the circuit, you can use the formula for calculating current in a parallel circuit. In a parallel circuit, the total current is equal to the sum of the individual branch currents.

Total Resistance (RT) = 1 / ((1/R1) + (1/R2) + (1/R3) + ...)

Here, R1 is the resistance of the lamp (151 ohms), R2 is the resistance of the electric heater (24 ohms), and R3 is the resistance of the fan (49 ohms).

So, the total resistance (RT) = 1 / ((1/151) + (1/24) + (1/49))

Solving this equation will give you the total resistance, RT. Once you have the total resistance, you can use Ohm's law to find the total current supplied to the circuit.

Total Current (IT) = Voltage (V) / Total Resistance (RT)

In this case, the voltage across the circuit is given as 121V. Substitute the values to calculate the total current.

The voltage across each branch in a parallel circuit is the same, equal to the voltage across the circuit (121V in this case). So, the voltage across the fan will be 121V.

To find the current in the lamp, you can use Ohm's law again.

Current (I) = Voltage (V) / Resistance (R)

Substituting the values, you can calculate the current in the lamp using the resistance of the lamp, which is 151 ohms.

Finally, to find the power expended in the heater, you can use the formula:

Power (P) = (Current)^2 x Resistance

Substitute the value of the current flowing through the electric heater, which you found earlier, and the resistance of the heater (24 ohms) to calculate the power expended.

I hope this explanation helps you find the answers to your questions!