What additional resistance must be connected with a 20 ohm lamp rated at 1 amp for use in a 120 volt circuit?

To determine the additional resistance required for the 20 ohm lamp rated at 1 amp in a 120-volt circuit, we start by calculating the voltage drop across the lamp at its rated current. According to Ohm's law (V = I × R), for the lamp:

Voltage across the lamp = Current × Resistance = 1 amp × 20 ohms = 20 volts.

This indicates that when the lamp is operating at its rated current, it will use 20 volts of the total 120 volts available in the circuit. To find the total resistance needed in the circuit to maintain the desired 120 volts, we use Ohm's law again:

Total required resistance = Total voltage / Desired current = 120 volts / 1 amp = 120 ohms.

Now we know the total resistance needed is 120 ohms, and our lamp provides 20 ohms of resistance. Therefore, to find the additional resistance that must be connected, we subtract the lamp's resistance from the total resistance required:

Additional resistance = Total required resistance - Lamp resistance = 120 ohms - 20 ohms = 100 ohms.

This calculation shows that to achieve the required voltage drop for proper operation in a 120-volt