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Given a circuit with a DC battery connected to a single resistor of resistance 6 ohms. The current through the resistor is I. If the resistance of the resistor is increased to 18 ohms then what is the ratio of the new electric current through the resistor to I? A)one fifteenth B)one twelfth C)one third D)three E)nine

User Lgriffiths
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1 Answer

5 votes

Given:

The initial resistance of the resistor, R=6 Ω

The resistance of the second resistor, R₀=18 Ω

The initial value of the current is I.

To find:

The ratio of new electric current through the circuit to the initial value of the current.

Step-by-step explanation:

From Ohm's law, The voltage of the battery before the resistance was increased is given by,


V=IR

The voltage of the battery is also given by,


V=I_0R_0

Where I₀ is the new electric current through the circuit.

From the above two equations,


\begin{gathered} IR=I_0R_0 \\ \Rightarrow(I_0)/(I)=(R)/(R_0) \end{gathered}

On substituting the known values,


\begin{gathered} (I_0)/(I)=(6)/(18) \\ =(1)/(3)\text{ } \end{gathered}

Final answer:

Thus the ratio of the new value of electricity to the old value of electricity is 1/3

Therefore the correct answer is option C.

User TaW
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