Question

Judge the equivalent resistance when following are connected in parallel
1. 1ohm and 10 raise to 6 ohm
2. 1ohm , 10 raise to 3 ohm and 10 raise to 6 ohm

Answer 1

Dear Student,

When the reistances are connected in parallel the total (equivalent) resistance of the circuit is calculated as


$\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}....\frac{1}{R_n}$, where R₁, R₂, R₃, ..., R_n are the individual resistances in the circuit and R is the equivalent resistance of the circuit.

for Q 1. R₁ = 1 $\Omega$ and R₂ = 10⁶ $\Omega$

$$\begin{gathered} \frac{1}{R}=1+\frac{1}{{10}^6}=\frac{{10}^6+1}{{10}^6} \\ orR=\frac{{10}^6}{{10}^6+1}=0.9999...\approx 1\Omega \end{gathered}$$

for Q 2. R₁ = 1 $\Omega$ , R₂ = 10³ $\Omega$ and R₃ = 10⁶ $\Omega$ ,

Then $$\begin{gathered} \frac{1}{R}=1+\frac{1}{{10}^3}+\frac{1}{{10}^6}=\frac{{\displaystyle {10}^6+{10}^3+1}}{{10}^6} \\ orR=\frac{{10}^6}{{10}^6+{10}^3+1}=0.999\approx 1\Omega \end{gathered}$$


Regards