A graph between current & time during charging of a capacitor by a battery in series with a resistor is shown. The graphs are drawn for two circuits. R1, C1 and V1 are the values of resistance, capacitance and EMF of the cell in one circuit and R2, C2 and V2 for another circuit respectively. If only two parameters (out of resistance, capacitance, EMF) are different in the two circuits. What is the correct option?

Engineering

Physics

Newtons Second Law of Motion

RC Circuit

Calculus

Question

A graph between current & time during charging of a capacitor by a battery in series with a resistor is shown. The graphs are drawn for two circuits. R₁, C₁ and V₁ are the values of resistance, capacitance and EMF of the cell in one circuit and R₂, C₂ and V₂ for another circuit respectively. If only two parameters (out of resistance, capacitance, EMF) are different in the two circuits. What is the correct option?

V₁ < V₂, C₁ < C₂, R₁ = R₂

V₁ > V₂, R₁ > R₂, C₁ = C₂

V₁ < V₂, R₁ < R₂, C₁ = C₂

V₁ = V₂, R₁ > R₂, C₁ > C₂

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$I = \frac{V}{R} e^{- t / (RC)}$
$∴ \log_{e} I = \log_{e} (\frac{V}{R}) - \frac{t}{RC}$
when $t = 0, \log_{e} I = \log_{e} (\frac{V}{R})$ which is same for both circuits. Hence, if one out of V and R is different, then another also has to be different.
∴ C₁ = C₂
Now, $∣ Slope ∣= \frac{1}{RC} is greater for (1)$
∴ R₁ < R₂
and hence V₁< V₂