What is the current flowing through the ideal Zener diode in the circuit below, if V1 = 12.1 V, R1 = 100 Ω, R2 = 102 Ω, and the breakdown voltage of the ideal Zener diode is Vz = 5.1 V?

A DC source supplies a voltage of 15 V to two series-connected resistors, one of which is 7.5 Ω and the other is an unknown resistor R. If the total circuit current is 1 A, determine the value of the unknown resistance R.

A resistor of 10 Ω is connected to a constant voltage source. When another resistor is connected in series with it, the current in the circuit becomes half of its initial value. Assuming the supply voltage remains unchanged, the resistance of the second resistor is _______.