Question

6r and 12r resistance are connected in parallel .this combination is connected in series with a 10v battery and 6r resistor what is the potential difference between the terminals of the 12r resistor? ​

Answer 1

Question

6Ω and 12Ω resistance are connected in parallel. This combination is connected in series with a 10V battery and 6Ω resistor. What is the potential difference between the terminals of the 12Ω resistor?

Solution -

Given that, 6Ω and 12Ω resistance are connected in parallel.

R1 = 6Ω and R2 = 12Ω

1/Rp = 1/R1 + 1/R2

1/Rp = 1/6 + 1/12

1/Rp = (2 + 1)/12

1/Rp = 3/12

1/Rp = 1/4

Rp = 4Ω

Now, the result which came after solving i.e. 4Ω resistor is connected in series with a 10V battery and 6Ω resistor. (R3 = 6Ω)

Rs = Rp + R3

Rs = 4 + 6

Rs = 10Ω

We have to find the potential difference between the terminals of the 12Ω resistor.

Now,

From Ohm's Law, we can say that,

V = IR

As per question, V = 10V and from the above calculations R = 10Ω.

So,

10 = I × 10

I = 10/10

I = 1 A

Now, we have I = 1A and R = 12Ω

{ As we have to find the potential difference between the terminals of the 12Ω resistor. }

V = IR or V = I × R2

V = 1 × 12

V = 12V

Answer 2

Correct Question :

6 ohm and 12 ohm resistance are connected in parallel .this combination is connected in series with a 10V battery and 6 ohm resistor what is the potential difference between the terminals of the 12 ohm resistor?

Answer :

Resistance connected in parallel ;

$\frac{1}{R} = \frac{1}{R1} + \frac{1}{R2}$

$\frac{1}{R} = \frac{1}{6} + \frac{1}{12} \\ \frac{1}{ R} = \frac{3}{12} \\ \frac{1}{R} = \frac{1}{4} \: ohm \\ R = 4 \: ohm$

Now, according to the question this combination is connected in series with a battery of 10V and resistor of 6 R. So, the total resistance now will be Rt=4+6 ohm =10 ohm.

Given potential difference of the battery =10V.

So, by using Ohm's law i.e V=IR. Where V is the potential difference, R is the resistance and I is the current supplied.

V=IR

10=I×10

I = 1 ampere.

Now, to find potential difference between the terminals of 12 ohm resistor;

V=IR

V=1×12

V=12 V.

Therefore, the potential difference between the terminals of the 12 ohm resistor is 12 Volts.