Question

Two resistors, R 1 and R 2 , are connected in parallel. R 2 =221.0 ohms, and the equivalent resistance of the combination is 120.7 ohms. What is the value of R 1 ? (Unit = ohm)

Answer 1

Step-by-step explanation:

When resistors are connected in parallel combination, then equivalent resistance is given by,

`\to \quad \bf{ (1)/(R_1) + (1)/(R_2) =(1)/(R_p)}`

Inserting values,

`\to \quad \bf { (1)/(R_1) + (1)/(R_2) =(1)/(R_p) } \\ \\ \to \quad \bf { (1)/(R_1) + (1)/(221) =(1)/(120.7) } \\ \\ \to \quad \bf { (221+R_1)/((R_1)(221)) =(1)/(120.7) } \\ \\ \to \quad \bf { (221+R_1)/(221R_1) =(1)/(120.7) } \\ \\ \to \quad \bf { 120.7(221+R_1) = 221R_1(1)} \\ \\ \to \quad \bf { 26674.7 + 120.7R_1= 221R_1} \\ \\ \to \quad \bf { 26674.7= 221R_1- 120.7R_1} \\ \\ \to \quad \bf { 26674.7 = 100.3R_1} \\ \\ \to \quad \bf { (26674.7 )/(100.3) =R_1} \\ \\ \to \quad\underline{\boxed{ \bf { 265.9 \; \Omega=R_1}}} \\`