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-->

`(1)/(Rs1) = (1)/(R1) + (1)/(R2) \\ \\ (1)/(Rs1) = (R1 + R2)/(R1R2) \\ \\ (1)/(Rs1) = (10 + 40)/(400) \\ \\ (1)/(Rs1) = (50)/(400) \\ \\ (1)/(Rs1) = (1)/(8) \\ \\ Rs1 = 8 Ω`

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

so total resistance-->

`(1)/(Rs2) = (1)/(R1) + (1)/(R2) + (1)/(R3) \\ \\ (1)/(Rs2) = (R1 + R2 +R3)/(R1R2R3) \\ \\ (1)/(Rs2) = (3+ 2 + 1)/(60) \\ \\ (1)/(Rs2) = (6)/(60) \\ \\ (1)/(Rs2) = (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 * I \\ \\ I = 0.66 \: A`