Question

There are two sets of resistors joined in series in a circuit. Set 1 has two resistors of 10Ω and 40Ω in parallel combination. Set 2 has three resistors of 20 Ω, 30 Ω and 60 Ω in parallel combination. A potential difference of 12 V is applied across the combination.​

Answer 1

$\huge\boxed{\fcolorbox{black}{red}{ QUESTION}}$

There are two sets of resistors joined in series in a circuit. Set 1 has two resistors of 10Ω and 40Ω in parallel combination. Set 2 has three resistors of 20 Ω, 30 Ω and 60 Ω in parallel combination. A potential difference of 12 V is applied across the combination.

$\orange{\underline{\huge{\bold{\textit{\green{\bf{GIVEN}}}}}}}$

Two set of Parallel resistors

Contains two resistors of --> 10Ω and 40Ω

Contains three resistors of --> 20 Ω, 30 Ω and 60Ω

Potential Difference Of 12 V

${\bold{\orange {To \: Find }}}$

Draw a circuit diagram to represent this arrangement Calculate

(a) the total resistance and

(b) the total current flowing in the circuit.

$\huge\mathbb{\red A \pink{N}\purple{S} \blue{W} \orange{ER}}$

FOR DIAGRAM REFER ATTACHMENT!

${\bold{\green{\star{\red {Part \: 1:- The \: Total \: Resistance }}}}}$

First we calculate the total resistance of each parallel combination:-

FIRST SET Contains two resistors of 10Ω and 40Ω

so total resistance-->

$\frac{1}{Rs1} = \frac{1}{R1} + \frac{1}{R2} \\ \\ \frac{1}{Rs1} = \frac{R1 + R2}{R1R2} \\ \\ \frac{1}{Rs1} = \frac{10 + 40}{400} \\ \\ \frac{1}{Rs1} = \frac{50}{400} \\ \\ \frac{1}{Rs1} = \frac{1}{8} \\ \\ Rs1 = 8 Ω$

SECOND SET Contains three resistors of 20 Ω, 30 Ω and 60Ω

so total resistance-->

$\frac{1}{Rs2} = \frac{1}{R1} + \frac{1}{R2} + \frac{1}{R3} \\ \\ \frac{1}{Rs2} = \frac{R1 + R2 +R3}{R1R2R3} \\ \\ \frac{1}{Rs2} = \frac{3+ 2 + 1}{60} \\ \\ \frac{1}{Rs2} = \frac{6}{60} \\ \\ \frac{1}{Rs2} = \frac{1}{10} \\ \\ Rs2 = 10Ω$

Now by having Total Resistance of Set one and set two we can add them by series formula.

$R = Rs1 + Rs2 \\ R = 8 + 10 = 18 \: Ω$

${\bold{\green{\star{\orange{Part \: 2:- The \: Total \: Current \: Flowing \: In \: The \: Circuit. }}}}}$

Total Resistance of the circuit = 18 Ω

Potential Difference Of the circuit = 12 V

So Total current-->

$V = IR \\ 12 = 18 \times I \\ \\ I = 0.66 \: A$