Question

A resistance of 10 ohms is connected in series with two resistances each of 15 ohms arrange in parallel. What resistance must be shunted across this parallel combination so that the total current shall be 1.5 amps with 20 volts applied? Draw a diagram

Answer 1

Explanations & Calculations

• The equivalent resistance of the $\small 15\Omega$ combination is

$\qquad\qquad \begin{aligned} \small &= \small \frac{15\times 15}{15+15}\\ &= \small 7.5\Omega \end{aligned}$

• Before a shunt resistor is connected, the current flowing in the circuit is,

$\qquad\qquad \begin{aligned} \small i&= \small \frac{20V}{10\Omega +7.5\Omega}\\ &= \small 1.143A \end{aligned}$

• After the shunt is connected the equivalent of the parallel combination would be

$\qquad\qquad \begin{aligned} \small &= \small \frac{7.5 R}{7.5+R}\\ \end{aligned}$

• Then the current would be

$\qquad\qquad \begin{aligned} \small i_1 &= \small \frac{20V}{10+\frac{7.5R}{7.5+R}} \end{aligned}$

• Since that current should be 1.5A ,

$\qquad\qquad \begin{aligned} \small 1.5A&= \small \frac{20}{10+\frac{7.5R}{7.5+R}}\\ \small 10+\frac{7.5R}{7.5+R}&= \small 13.333\\ \small R &= \small 5.9989\Omega\\ &\approx \small 6\Omega \end{aligned}$

• It is the resistance needed to be shunted to the parallel combination
• This reduces the equivalent resistance ($\small \because i_1>i$ ) of the entire circuit.