Question

Consider a delta connection of resistors and its equivalent star connection as shown below. If all elements of the delta connection are scaled by a factor k, k > 0, the elements of the corresponding star equivalent will be scaled by a factor of

• A. $k^2$
• B. k
• C. 1/k
• D. $\sqrt{k}$

Answer 1

The correct option is B k

$R_A=\frac{R_b{R}_c}{R_a+R_b+R_c}$

$R_a^{{}^{\prime }}=k{R}_a$

$R_b^{{}^{\prime }}=k{R}_b$

$R_c^{{}^{\prime }}=k{R}_c,$

$R_A^{{}^{\prime }}=\frac{k{R}_b.k{R}_c}{k{R}_a+k{R}_b+k{R}_c}=\frac{k^2{R}_b{R}_c}{k(R_a+R_b+R_c)}$

$=k\times \frac{R_b{R}_c}{R_a+R_b+R_c}$

$R_A^{{}^{\prime }}=k{R}_A$