Final answer:
In a parallel circuit, the total resistance can be calculated using the reciprocals of the individual resistances. The value of resistor R is infinity, indicating an open circuit.
Step-by-step explanation:
In a parallel circuit, the reciprocal of the total resistance is equal to the sum of the reciprocals of the individual resistances. So, for a parallel circuit with resistors of 15 Ω and 7 Ω, the total resistance (Req) can be calculated as:
Req = (1/15) + (1/7)
Req = 0.06667 + 0.14286
Req = 0.20953
Now, to find the value of resistor R, we subtract the sum of the reciprocals of the given resistors from the reciprocal of the total resistance:
(1/R) = (1/Req) - (1/15) - (1/7)
(1/R) = 0.20953 - 0.06667 - 0.14286
(1/R) = 0.0
Since the reciprocal of R is 0, R must be infinity. Therefore, resistor R has an open circuit, so none of the given options for its value (A, B, C, D, E) are correct.