A 30V, 40 w lamp is to be operated on a 120 V DC lines. For proper glows, how much resistance in `Omega` should be connected in series with the lamp?

Options

A. `67.5Omega`
B. `4.75Omega`
C. `75.6Omega`
D. none

Answer

To solve the problem of determining the resistance that should be connected in series with a 30V, 40W lamp to operate it on a 120V DC line, we can follow these steps:

### Step 1: Determine the current drawn by the lamp
The power \( P \) of the lamp is given as 40W and the voltage \( V \) across the lamp is 30V. We can use the formula for power:

\[ P = V \times I \]

Rearranging this to find the current \( I \):

\[ I = \frac{P}{V} \]

Substituting the values:

\[ I = \frac{40W}{30V} = \frac{4}{3} \, A \]

### Step 2: Calculate the resistance of the lamp
Using Ohm's law, the resistance \( R_L \) of the lamp can be calculated as:

\[ R_L = \frac{V}{I} \]

Substituting the values we have:

\[ R_L = \frac{30V}{\frac{4}{3} A} = 30V \times \frac{3}{4} = 22.5 \, \Omega \]

### Step 3: Determine the total voltage and current in the circuit
The total voltage supplied is 120V. The current flowing through the circuit is the same as the current through the lamp, which we calculated as \( \frac{4}{3} A \).

### Step 4: Calculate the total resistance required for the circuit
Using Ohm's law again, the total resistance \( R_{total} \) required for the circuit can be calculated as:

\[ R_{total} = \frac{V_{total}}{I} \]

Substituting the values:

\[ R_{total} = \frac{120V}{\frac{4}{3} A} = 120V \times \frac{3}{4} = 90 \, \Omega \]

### Step 5: Calculate the required series resistance
The total resistance in the circuit is the sum of the lamp's resistance and the external resistance \( R \) that we need to find:

\[ R_{total} = R_L + R \]

Rearranging this gives:

\[ R = R_{total} - R_L \]

Substituting the values we calculated:

\[ R = 90 \, \Omega - 22.5 \, \Omega = 67.5 \, \Omega \]

### Final Answer
The resistance that should be connected in series with the lamp is:

\[ \boxed{67.5 \, \Omega} \]