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Five resistors of different resistances are connected together as shown in the figure.

A 12 V battery is connected to the arrangement.

Five resistors of different resistances are connected together as shown in the figure. A 12 V battery is connected to the arrangement. Calculate total resistance in the circuit, the total current flowing in the circuit. Physics Sample Paper Solved ICSE Class 10.

Calculate

(a) total resistance in the circuit.

(b) the total current flowing in the circuit.

Current Electricity

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Answer

(a) In the circuit, there are three parts. In the first part two resistors of 10 Ω and 40 Ω are connected in parallel. In parallel, the equivalent resistance is Rp, then

1RP=110+1401RP=4+1401RP=540⇒RP=405=8Ω\dfrac{1}{RP} = \dfrac{1}{10} + \dfrac{1}{40} \\[0.5em] \dfrac{1}{RP} = \dfrac{4 + 1}{40} \\[0.5em] \dfrac{1}{RP} = \dfrac{5}{40} \\[0.5em] \Rightarrow RP = \dfrac{40}{5} = 8 Ω \\[0.5em]

In the second part three resistors of 30, 20 and 60 Ω are connected in parallel. In parallel, the equivalent resistance is R'p, then

1RP′=130+120+1601RP′=2+3+1601RP′=660⇒RP′=606=10Ω\dfrac{1}{R'P} = \dfrac{1}{30} + \dfrac{1}{20} + \dfrac{1}{60} \\[0.5em] \dfrac{1}{R'P} = \dfrac{2 + 3 + 1}{60} \\[0.5em] \dfrac{1}{R'P} = \dfrac{6}{60} \\[0.5em] \Rightarrow R'P = \dfrac{60}{6} = 10 Ω \\[0.5em]

In the third part, Rp and R'p are in series, the equivalent resistance is R then 8 + 10 = 18 Ω

Hence, total resistance = 18 Ω

(b) From Ohm's Law : V = IR

Substituting the values we get, 12 = I x 18

∴ I = 1218\dfrac{12}{18} = 0.67 A.

Hence, total current = 0.67 A

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