Three resistors having resistances r₁ , r₂ and r₃ are connected as shown in the given circuit. The ratio i₃/i₁ of currents in terms of resistances used in the circuit is : 1. r₁/r₂+r₃ 2. r₂/r₂+r₃ 3. r₁/r₁+r₂ 4. r₂/r₁+r₃

Answer: 2. r₂/r₂+r₃ Key idea: r₂ and r₃ are in parallel, and the current i₁ splits in inverse ratio of resistances (current divider). i₃=i₁·r₂/r₂+r₃⇒i₃/i₁=r₂/r₂+r₃ . Option 2.

Topic: Kirchhoff's laws and applications· Current Electricity

Three resistors having resistances r_1, r_2 and r_3 are connected as shown in the given circuit. The ratio i_3/i_1 of currents in terms of resistances used in the circuit is :

Three resistors having resistances \(r_1\), \(r_2\) and \(r_3\) are connected as shown in the given circuit. The ratio \(\frac{i_3}{i_1}\) of currents in terms of resistances used in the circuit is :

r1 in series with parallel r2 and r3, currents i1, i2, i3

1. \(\frac{r_1}{r_2+r_3}\)

2. \(\frac{r_2}{r_2+r_3}\)

3. \(\frac{r_1}{r_1+r_2}\)

4. \(\frac{r_2}{r_1+r_3}\)

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Answer: 2. \(\frac{r_2}{r_2+r_3}\)

Key idea: \(r_2\) and \(r_3\) are in parallel, and the current \(i_1\) splits in inverse ratio of resistances (current divider).

\(i_3=i_1\cdot\dfrac{r_2}{r_2+r_3}\Rightarrow\dfrac{i_3}{i_1}=\dfrac{r_2}{r_2+r_3}\). Option 2.

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Three resistors having resistances r_1, r_2 and r_3 are connected as shown in the given circuit. The ratio i_3/i_1 of currents in terms of resistances used in the circuit is :

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