Astudent constructed a series circuit consisting of a 12.0-volt battery, a 10.0-ohm lamp, and a
resistor. the circuit does not contain a voltmeter or an ammeter. when the circuit is operating, the
total current through the circuit is 0.50 ampere.
determine the equivalent resistance of the circuit.

I thought you were going to ask for the resistance of the unknown
series resistor.  Since you only want the equivalent resistance of the
circuit, you don't even need to know the resistance of the lamp.

I = E / R

Current through the circuit = (voltage of the battery) / (circuit resistance).
  
                                                  0.5 = (12) / R

Multiply each side by  'R' :    (0.5) R = 12

Multiply each side by  2 :      R = 24 ohms

(Since the resistance of the lamp is 10 ohms, the
unknown series resistor is the other 14 ohms.)

    5.5 n======    assuming that      we have      m = 0.145 kg    a = 38 m/s²therefore    5.51 n, but two significant figures.final answer: 5.5 n