Question

In this circuit the resistance R1 is 7 Ω and R2 is 3 Ω. If this combination of resistors were to be replaced by a single resistor with an equivalent resistance, what should that resistance be? Give your answer in units of Ohms (LaTeX: \OmegaΩ).

Answer 1

Answer:

Series combination:

Equivalent resistance =10Ω

Parallel combination:

Equivalent resistance $=\frac{21}{10} \Omega$

Explanation:

Resistance: Resistance is the ratio of voltage to the current.

$R=\frac{V}{I}$

R = resistance

I = current

V= potential difference(voltage)

There are two types of resistance combinations.

1. series combination
2. parallel combination.

Series combination: If the ending point of one resistance is connected to the starting point of other resistance that combination is known as series combination.

If R₁,R₂ and R₃  are connected in series combination.

Then equivalent resistance = R₁+R₂+R₃

Parallel combination: If the ending point and the starting point of the all resistance are the same points that combination is known as parallel combination.

If R₁,R₂ and R₃  are connected in parallel combination.

Then equivalent resistance  $\frac{1}{R}= \frac{1}{R_1}+ \frac{1}{R_2}+\frac{1}{R_3}$

Here R₁=7Ω and     R₂=3Ω

If R₁ and R₂  connected in series combination

Then equivalent resistance = (7+3) Ω

                                            =10Ω

If R₁ and R₂  connected in parallel combination

Then equivalent resistance $=\frac{1}{(\frac{1}{7} +\frac{1}{3})} \Omega$

                                              $=\frac{21}{10} \Omega$