Question

A student, using the same two resistors, battery, ammeter and voltmeter, sets up two circuits, connecting the two resistors, first in series and then in parallel. If the ammeter and voltmeter readings in the two cases, are (I1, I2) and (V1, V2) respectively, he is likely to observe that
(1) I1 = I2 but V1 ≠ V2
(2) I1 < I2 but V1 = V2
(3) I1 > I2 but V1 = V2
(4) I1 = I2 and V1 = V2

Answer 1

Answer:

(4) |1=|2,but v1=V2 is correct answer

Answer 2

The student is likely to observe that (2) I1 < I2 but V1 = V2.

Explanation:

From question, we can understand that the resistors connected are same.

Let the resistance of the resistor R1 and R2 be R

Resistor in Series:

Equivalent resistance is:

Rs = R + R = 2R

Now, the reading in voltmeter and ammeter is V1 and I1.

According to Ohm's law, the voltage is given as:

V1 = (2R) × I1 = 2R.I1 → (1)

Resistor in Parallel:

Equivalent resistance is:

Rp = 1/R + 1/R = 2/R

Now, the reading in voltmeter and ammeter is V2 and I2.

According to Ohm's law, the voltage is given as:

V2 = (2/R) × I2 = R.I2/2 → (2)

Now, on comparing equation (1) and (2), we get,

$\bold{\frac{V1}{V2}=\frac{2R \times I1}{(R.I2/2)}}$

$\bold{\frac{V1}{V2}=\frac{4I1}{12}}$

From the options given, the different power is not possible. So, considering the powers are equal, then the equation becomes,

I2 = 4I1

From above equation, the current drawn in the parallel is four times larger than current drawn in series. So, option (2) is correct answer.