Final answer:
The equivalent resistance (Req) for two resistors in parallel is found by the sum of the reciprocals of each resistance, resulting in approximately 4.77 Ω. For two resistors in series, it's the sum of the resistances, resulting in 2.45 MΩ.
Step-by-step explanation:
To explain how to obtain the equivalent resistance (Req) of circuit configurations, we have to look into the way resistors are combined. For resistors in series, Req is simply the sum of the resistances. In contrast, for resistors in parallel, the reciprocal of Req is the sum of the reciprocals of each individual resistance.
In our first example, we have two resistors in parallel with resistance values of 15 Ω and 7 Ω. To find the equivalent resistance, we use the formula:
1/Req = 1/R1 + 1/R2
1/Req = 1/15 + 1/7
1/Req = 7/105 + 15/105
1/Req = 22/105
Req = 105/22
Req ≈ 4.77 Ω
For the second example, we have two resistors in series with resistance values of 750 kΩ and 1.7 MΩ. The equivalent resistance is simply the sum of the two:
Req = R1 + R2
Req = 750 kΩ + 1.7 MΩ
Req = 750 kΩ + 1700 kΩ
Req = 2450 kΩ
Req = 2.45 MΩ
Understanding how to calculate equivalent resistance is crucial for circuit analysis and affects how current flows through a circuit.