Two identical resistors each of resistance 10 ohm are connected in: (i) Series , (ii) Parallel , in turn to a battery of 6V . Calculate the ratio of power consumed by the combination of resistor in the two cases.
\n30656"
Given:
Two resistances of 10 ohm each are connected in Series and then Parallel.
Voltage = 6 V.
To find: The ratio of power consumed in the two cases
Solution:
We know power consumed by a resistor $ = \frac{Voltage^2}{Resistance}$
Or
$P = \frac{V^2}{R}$
Series case:
Effective Resistance R = R1 + R2
= 10 + 10
So effective resistance R = 20 ohm
Power $P = \frac{V^2}{R}$
$= \frac{6^2}{20} = 1.8$
Power = 1.8 watt
Parallel case:
We can find effective resistance using the formula
$\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2}$
$\frac{1}{R} = \frac{1}{10} + \frac{1}{10}$
$\frac{1}{R} = \frac{2}{10}$
So effective resistance, $R = \frac{10}{2}$
= 5 ohm
Power $P = \frac{V^2}{R}$
$= \frac{6^2}{5} = 7.2$
Power = 7.2 watt
Ratio of power in the given cases = $\frac{1.8\ watt}{ 7.2 \ watt}$
= $\frac{1}{4}$
So ratio of power consumed is $\frac{1}{4}$
Related Articles Two identical resistors, each of resistance 15 W, are connected in (i) series, and (ii) parallel, in turn to a battery of 6 V. Calculate the ratio of the power consumed in the combination of resistors in each case.
(a) Three resistors of resistances R1, R2 and R3 are connected (i) in series, and(ii) in parallel. Write expressions for the equivalent resistance of the combination in each case.(b) Two identical resistors of 12 $\Omega$ each are connected to a battery of 3 V. Calculate the ratio of the power consumed by the resulting combinations with minimum resistance and maximum resistance.
N resistors of resistance R are connected in series and than in parallel .What will be the ratio of resistance in both the cases?
How to find the resistance of 'n' number of resistors connected in parallel combination?
If two resistors of value R are connected in series and then in parallel, what is the difference in equivalent resistance in both cases?
How to calculate the resistances of n number of resistors connected in parallel combination?
(a) Two lamps rated 100 W, 220 V, and 10 W, 220 V are connected in parallel to 220 V supply. Calculate the total current through the circuit.(b) Two resistors X and Y of resistances 2Ω and 3Ω respectively are first joined in parallel and then in series. In each case, the voltage supplied is 5 V.(i) Draw circuit diagrams to show the combination of resistors in each case.(ii) Calculate the voltage across the 3Ω resistor in the series combination of resistors.
(a) Three resistors R1, R2 and R3 are connected in parallel and the combination is connected to a battery, ammeter, voltmeter and key. Draw suitable circuit diagram and obtain an expression for the equivalent resistance of the combination of the resistors.(b) Calculate the equivalent resistance of the following network:"\n
To determine equivalent resistance of resistors when connected in series and in parallel
Compare the power used in the $2 \Omega$ resistor in each of the following circuits:$(i)$ a $6\ V$ battery in series with $1\ \Omega$ and $2\ \Omega$ resistors, and$(ii)$ a $4\ V$ battery in parallel with $12\ \Omega$ and $2\ \Omega$ resistors.
If two resistors of 25Ω and 15Ω are joined together in series and then placed in parallel with a 40Ω resistor, the effective resistance of the combination is:(a) 0.1Ω (b) 10Ω (c) 20Ω (d) 40Ω
Draw a schematic diagram of a circuit consisting of a battery of 3 cells of 2 V each, a combination of three resistors of 10 W, 20 W, and 30 W 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.
The resistance of two conductors in parallel is \( 12 \Omega \) and in series is \( 50 \Omega \). Find the resistance of each conductor.
A hot plate of an electric oven connected to a $220\ V$ line has two resistance coils A and B, each of $24\ Ω$ resistance, which may be used separately, in series, or in parallel. What are the currents in the three cases?
When a 12 V battery is connected across an unknown resistor, there is a current of 2.5 mA in the circuit. Find the value of the resistance of the resistor.
Kickstart Your Career
Get certified by completing the course
Get Started