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.

Cyclotrons are widely used in nuclear medicine for producing short-lived radioactive isotopes. these cyclotrons typically accelerate h- (the hydride ion, which has one proton and two electrons) to an energy of 5 mev to 20 mev. this ion has a mass very close to that of a proton because the electron mass is negligible—about 1 2000 of the proton’s mass. a typical magnetic field in such cyclotrons is 1.9 t. (a) what is the speed of a 5.0-mev h-? (b) if the h- has energy 5.0 mev and b = 1.9 t, what is the radius of this ion’s circular orbit?