Question

two identical resistors each of resistance 12 ohm are connected
i. in series
ii. in parallel
with 10A current and battery of 6V? calculate ratio of power consumed in combination of resistors in the two cases

Answer 1

Answer:Resistance, R1 = R2 = 15Ω

Voltage, V = 6V.

To find: The ratio of power consumed in the combination of resistors in each case, PS/PR.

Solution: (i) Series case

In series, total resistance is given as-

RS = R1 + R2

RS = 15 + 15

RS = 30Ω

Thus, the total resistance in series, RS is 30Ω

Now,

We know that, power consumed by a resistor is given as-

Power=Voltage2/Resistance Or,  P=V2/R

Substituting the value of V and R we get-

PS = 62/30

PS = 36/30

PS = 1.2W

Thus, the power consumed in series, PS is 1.2 watt.

(ii) Parallel case:

In parallel, total resistance is given as-

1/RP = 1/R1  + 1/R2

1/RP  = 1/15 + 1/15

1/RP  = 1 + 1/15

1/RP  = 2/15

RP  = 15/2

RP  = 7.5Ω

Thus, the effective resistance in parallel, RP is 7.5Ω

Now,

We know that, power consumed by a resistor is given as-

Power = Voltage2/Resistance Or,  P=V2/R

Substituting the value of V and R we get-

PR = 62/7.5

PR = 36/7.5

PR = 360/75

PR = 4.8W

Thus, the power consumed in parallel, PR is 4.8 watt.

Ratio of power consumed in the two combinations,

PS/PR = 1.2 W/4.8

W = 1/4 = 1:4

Thus, the ratio of power consumed in the combination of resistors in each case is 1:4.

Explanation: :