If in Fig. 12.12, R
_{
1
}
= 10 Ω, R
_{
2
}
= 40 Ω, R
_{
3
}
= 30 Ω, R
_{
4
}
= 20 Ω, R
_{
5
}
= 60 Ω,and a 12 V battery is connected to the arrangement. Calculate

(a) the total resistance in the circuit, and

(b) the total current flowing in the circuit.

Transcript

Example 12.9 If in Fig. 12.12, R1 = 10 Ω, R2 = 40 Ω, R3 = 30 Ω, R4 = 20 Ω, R5 = 60 Ω, and a 12 V battery is connected to the arrangement. Calculate (a) the total resistance in the circuit, and (b) the total current flowing in the circuit.
Given,
R1 = 10 Ω
R2 = 40 Ω
R3 = 30 Ω
R4 = 20 Ω
R5 = 60 Ω
Potential difference = 12 V
Finding total Resistance (R)
Here,
R1 and R2 are connected in parallel
and R3, R4 & R5 are connected in parallel
Suppose we replace R1 and R2 with an equivalent resistor R’
and we replace R3, R4 and R5 with an equivalent resistor R’’
In parallel connection,
1/𝑅_𝑝 = 1/𝑅_1 + 1/𝑅_2 + 1/𝑅_3 + … … …
Calculating R’
1/𝑅′ = 1/𝑅_1 + 1/𝑅_2
1/𝑅′ = 1/10 + 1/40
1/𝑅′ = (4 + 1)/40
1/𝑅′ = 5/40
1/𝑅′ = 1/8
R’ = 8 Ω
Calculating R’’
1/𝑅^′′ = 1/𝑅_3 + 1/𝑅_4 + 1/𝑅_5
1/𝑅^′′ = 1/30 + 1/20 + 1/60
1/𝑅^′′ = (2 + 3 +1)/60
1/𝑅^′′ = 6/60
1/𝑅^′′ = 1/10
R’’ = 10 Ω
Replacing R1 and R2 by R’
and Replacing R3, R4 and R5 by R’’
Now, R’ and R’’ are connected in series.
In series connection,
Rs = R1 + R2 + … …
∴ Net Resistance = R = R’ + R’’
= 8 Ω + 10 Ω
= 18 Ω
(b) Finding total current
By ohm’s law,
V = I R
𝑉/𝑅 = I
I = 𝑉/𝑅
I = 12/18
I = 2/3
I = 0.67 A
Total resistance in circuit is 18 Ω
Total current in circuit is 0.67 A

CA Maninder Singh is a Chartered Accountant for the past 14 years and a teacher from the past 18 years. He teaches Science, Economics, Accounting and English at Teachoo

Hi, it looks like you're using AdBlock :(

Displaying ads are our only source of revenue. To help Teachoo create more content, and view the ad-free version of Teachooo... please purchase Teachoo Black subscription.

Please login to view more pages. It's free :)

Teachoo gives you a better experience when you're logged in. Please login :)

Solve all your doubts with Teachoo Black!

Teachoo answers all your questions if you are a Black user!