Name: Resistivity and Its Temperature Dependence
Uploaded: 2019-07-19
Duration: 5 min 51 s
Description: In this video, we will discuss the resistivity of different materials and the variation of resistivity with temperature. Let us watch this video and learn.

Question

The figure given below shows an electric circuit in which current flows from a

6 V

battery through two resistors.

(a) Are the resistors connected in series with each other or in parallel?
(b) For each resistor, state the p.d. across it.
(c) The current flowing from the battery is shared between the two resistors. Which resistor will have a bigger share of the current?
(d) Calculate the effective resistance of the two resistors.
(e) Calculate the current that flows from the battery.

Accepted Answer

(a) The resistors are connected in parallel. This can be identified by checking the paths where the current can flow. In parallel connection, the current has more than one path to flow.

(b) In a parallel combination of resistance, the voltage remains the same across each resistor and it will be same as the supply voltage in this case. Therefore, the p.d across each resistor is $6 V .$

(c) The $2 Ω$ resistor will have a bigger share of the current since resistance is inversely proportional to the current in parallel combination.
Assume $I_{1}$ is the current through $2 Ω$ and $I_{2}$ is the current through $3 Ω$ resistor,
$I_{1} = \frac{6}{2} = 3 A, I_{2} = \frac{6}{3} = 2 A$

(d) The effective resistance of the parallel combination is:
$\frac{1}{R} = \frac{1}{R_{1}} + \frac{1}{R_{2}}$
$\frac{1}{R} = \frac{1}{2} + \frac{1}{3}$
$\frac{1}{R} = \frac{3 + 2}{6}$
$\frac{1}{R} = \frac{5}{6}$
$R = \frac{6}{5} Ω$
$R = 1.2 Ω$

(e) The current flowing through the battery, $I = I_{1} + I_{2} = 5 A$ . In parallel combination, the net current is the sum of the current through the individual resistors.

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