Question

The voltage of the battery is 12 V, and the values of the resistances are: R₁ = 5 ohms, R₂ = 10 ohms, R₃ = 15 ohms, and R₄ = 20 ohms.

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11)  R₁ and R₄ are in:

parallel

series

neither

Answer 1

In a parallel connection the voltage drop across the resistors will be the same and in a series connection the current flowing through the resistors will be the same.

Now, if we analyse the voltage drop across R₁ will be the source voltage, but the voltage across the R₄ will be the voltage across R₂. Hence, as the voltages are different, R₁ and R₄ are not connected in parallel.

Now, R₁ and R₄ are in different loops and the current flowing through R₁ and R₄ are also not the same as per kirchoffs loop rule. Hence, as the currents are different, R₁ and R₄ are not connected in series.

Therefore, the answer is neither. (Infact, R₁ is connected in series with parallel combination of R₂ and R₄)