Question

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

Answer 1

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.

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,

$\begin{gathered} IR=I_0R_0 \\ \Rightarrow\frac{I_0}{I}=\frac{R}{R_0} \end{gathered}$

On substituting the known values,

$\begin{gathered} \frac{I_0}{I}=\frac{6}{18} \\ =\frac{1}{3}\text{ } \end{gathered}$

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.