In a circuit, a 10-volt battery and three resistors ( R1 = 2 Ω ), ( R2 = 3 Ω), and ( R3 = 6 Ω) are connected in parallel to each other. Which of the following is the correct value of effective resistance ( Re ) and current I flowing through the circuit?
( Re = 1 Ω I = 10 A )
To find the effective resistance (Re) of resistors connected in parallel, we use the formula:
1/Re=1/R1+1/R2+1/R3
Substitute the given values (R1=2Ω, R2=3Ω, R3=6Ω):
1/Re=1/2+1/3+1/6
Calculate the right-hand side:
=3/6+2/6+1/6=6/6=1
Thus, Re=1 Ω.
Next, use Ohm's Law to find the current (I):
I=V/Re
Given the battery voltage V=10V and Re=1Ω, substitute these values into Ohm's Law:
I=10/1=10A
Thus, the effective resistance is Re=1 Ω, and the current flowing through the circuit is I=10 A.
Important Questions from Resistance and Resistivity
Which of the following metals has the lowest electrical resistivity?
When electric current is passed through a wire, the amount of heat produced in a wire depends upon _______.
I. Length
II. Thickness
A uniform wire of resistance 9Ω is bent in the form of an equilateral triangle. Find the effective resistance across a side of the triangle.
The value of carbon resistance is 54 × 103 Ω. The percentage tolerance is 5%. What is the colour code sequence of carbon resistance?
Which of the following relations are wrong?
I. The specific conductance is given by the relation \(k = \frac{1}{R}\left( {l/A} \right)\)
II. The equivalent conducting is given by the relation \(\lambda = \frac{{100\;K}}{C}\)
III. The specific resistance is given by the relation \(\rho = \frac{{Rl}}{A}\)
