Question

when 15 ohms resistors joined in series and parallel with 6 volt in the circuit find the ratios of their power​

Answer 1

Answer:

Explanation:

If no of resistors is 2 then

Ratio of power became 4:1

Answer 2

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( i ) When connected in parallel, the equivalent resistance is:

$\displaystyle{\frac{1}{R_p}}$ =$\displaystyle{\frac{1}{15}}$ + $\displaystyle{\frac{1}{15}}$

$\displaystyle{\frac{R_p}}$ = $\displaystyle{\frac{2}{15}}$

${R}_{p}$ = $\frac{15}{2}$

The current ( I ) = $\frac{V}{R}$ → Ohm's law

I = $\displaystyle{\frac{6}{15}}× 2$

I = $\displaystyle{\frac{12}{15}}$

Power consumed = I²R

= $\displaystyle{\frac{12}{15}}$² × $\displaystyle{\frac{15}{2}}$

= $\displaystyle{\frac{72}{15}}$

$<hr size = "2">$

( ii )When connected in series, the equivalent resistance is:

${R}_{s}$ = 15 + 15

${R}_{s}$ = 30

Power consumed = $\displaystyle{\bold{\frac{{V}^{2}}{R}}}$

= $\displaystyle{\frac{{6}^{2}}{30}}$

= $\displaystyle{\frac{6}{5}}$$<hr size ="2">$

Ratio of power consumed = power consumed in (ii) / power consumed in (i)

→ $\displaystyle{\frac{6}{5}}$÷$\displaystyle{\frac{72}{15}}$

→$\frac{1}{4}$

→ 1 : 4