Question

Given: Resistor 1= 5 ohm, Resistor 2= 12 ohm, resistor 3= 6 ohm, resistor 4= 6 ohm and resistor 5= 30 ohm.

1. Suppose the four resistors are connected in parallel. What is the resistance of the combined resistors?

2. Suppose the four resistors are connected in parallel. Find (a) equivalent resistance (b) current flowing through each resistor (c) voltage across each resistor and (d) power dissipated by each resistor.

3. Find the equivalent resistance of the combination of resistance shown.

Answer 1

Given resistance are:-

$R_1=5\Omega, R_2=12\Omega,R_3=6\Omega, R_4=6\Omega,R_5=30\Omega$

(i) As The resistors are connected in Parallel

$\dfrac{1}{R_{eqv.}}=\dfrac{1}{R_1}+\dfrac{1}{R_2}+\dfrac{1}{R_3}+\dfrac{1}{R_4}+\dfrac{1}{R_5}$

$=\dfrac{1}{5}+\dfrac{1}{12}+\dfrac{1}{6}+\dfrac{1}{6}+\dfrac{1}{30}$

$=\dfrac{12+5+10+10+2}{60}=\dfrac{39}{60}$

$R_{eqv.}=\dfrac{60}{39}=1.538\Omega$

(ii) If The four resistor are connected in parallel then

$\dfrac{1}{R_{eqv.}}=\dfrac{1}{R_1}+\dfrac{1}{R_2}+\dfrac{1}{R_3}+\dfrac{1}{R_4}$

$=\dfrac{1}{5}+\dfrac{1}{12}+\dfrac{1}{6}+\dfrac{1}{6}$

$=\dfrac{12+5+10+10}{60}=\dfrac{37}{60}$

$R_{eqv.}=\dfrac{60}{37}=1.62\Omega$

(a) Let the voltage across the circuit is V, As all the resistance are connected in Parallel

So Volteage Across each resistor is V.

(b) Current in $R_1=\dfrac{V}{5} A$

Current in $R_2=\dfrac{V}{12} A$

Current in $R_3=\dfrac{V}{6} A$

Current in $R_4=\dfrac{V}{6} A$

Current in $R_5=\dfrac{V}{30} A$

(c) Power disisipiaton in $R_1=\dfrac{V^2}{5}$ Watt

Power disisipiaton in $R_2=\dfrac{V^2}{12}$ Watt

Power disisipiaton in $R_3=\dfrac{V^2}{6}$ Watt

Power disisipiaton in $R_4=\dfrac{V^2}{6}$ Watt

Power disisipiaton in $R_5=\dfrac{V^2}{30}$ Watt

(iii) Equivalent resistance is same as the combined i.e. $1.538\Omega$