A 24-volt relay coil draws 48mA at rated voltage. A resistance check showed the coil to have 100ohms resistance. How much resistance should be added to the circuit in order to operate the relay coil at 120 volts?

Here is my solution:

\[ 24V/48mA= 500ohms =Z \]

\[ R=100ohms \]

\[ R^2+X^2=Z^2 \]

\[ sqrt(100^2-500^2)=X \]

\[ sqrt(240000)=489ohms \]

\[ 120V/48mA=2500ohms \]

\[ Z=2500ohms

X=489ohms\]

\[ sqrt(Z^2-X^2=R \]

\[ sqrt(6250000-239121)=2451ohms=R \]

\[ 2451ohms-100ohms(already in circuit)=2351.71ohms \]

Hello,

I wanted to see If I have the correct answer.

Thank you

Here is my solution:

\[ 24V/48mA= 500ohms =Z \]

\[ R=100ohms \]

\[ R^2+X^2=Z^2 \]

\[ sqrt(100^2-500^2)=X \]

\[ sqrt(240000)=489ohms \]

\[ 120V/48mA=2500ohms \]

\[ Z=2500ohms

X=489ohms\]

\[ sqrt(Z^2-X^2=R \]

\[ sqrt(6250000-239121)=2451ohms=R \]

\[ 2451ohms-100ohms(already in circuit)=2351.71ohms \]

Hello,

I wanted to see If I have the correct answer.

Thank you

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