Question

What is the equivalent resistance between points a and b of the six resistors shown in the figure below? (Let Ra = 2.30Ω, Rb = 5.70Ω, and Rc = 6.30 Ω.)

Answer 1

The formula to calculate equivalent resistance for a series combination of resistors is $R=R_{1}+R_{2}+R_{3}+R_{4}+......$

The formula to calculate equivalent resistance for a parallel combination of resistors is $R=\left (\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}}+\frac{1}{R_{4}}+...... \right )^{-1}$

Now,

The resistors of resistance Ra, 2 ohm and 4.4 ohm are in series, their equivalent resistance is $R_{1}=R_{a}+2+4.4 = 2.3+2+4.4 = 8.7 \Omega$

This R1 is in parallel to Rb, therefore, their equivalent resistance is $R_{2}=\left (\frac{1}{R_{1}}+\frac{1}{R_{b}} \right )^{-1} = \left (\frac{1}{8.7}+\frac{1}{5.7} \right )^{-1}=3.44\Omega$

This R2 is in series with Rc and 3.7 ohm resistor, therefore their equivalent resistance is $R= R_{2}+R_{c}+3.7 = 3.44+6.3+3.7=13.44\Omega$

Therefore, the equivalent resistance between the points "a" and "b" is 13.44 ohm. [answer]