Draw a schematic diagram of a circuit consisting of a battery of 3 cells of $2\text{ V}$ each, a combination of three resistors of $10\Omega$, $20\Omega$ and $30\Omega$ connected in parallel, a plug key and an ammeter, all connected in series. Use this circuit to find the value of the following:

(a) Current through each resistor

(b) Total current in the circuit

(c) Total effective resistance of the circuit

OR

Two identical resistors, each of resistance $15\Omega$, are connected in (i) series, and (ii) parallel, in turn to a battery of $6\text{ V}$. Calculate the ratio of the power consumed in the combination of resistors in each case.

This question tests the fundamental understanding of series and parallel combinations of resistors, Ohm's law, and electric power.

1. Parallel Combination Characteristics:

• The potential difference across each parallel branch is identical and equal to the source voltage.
• The total current is the sum of individual branch currents.
• The equivalent resistance is always less than the smallest individual resistance in the combination ($5.45\Omega < 10\Omega$).

1. Power Consumption in Combinations:

• For a constant voltage source, power is inversely proportional to the equivalent resistance ($P \propto 1/R$).
• Since $R_s = 2R$ and $R_p = R/2$, the ratio of resistances is $R_s / R_p = 4$.
• Consequently, the ratio of power consumed is $P_s / P_p = 1/4$.