Question

यदि 1000 रु० का मिश्रधन 2 वर्ष में 1102.50 हो जाता है तो ब्याज की दर ज्ञात कीजिए।
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Answer 1

Let A be the plate area and d be the distance between the plates,

1) A dielectric slab of thickness t is inserted,

Due to polarization inside the dielectric electric field will reduce,

So outside of dielectric, field = E₀

inside of dielectric, field = E = E₀/k

where k is the dielectric constant,

So the net potential will be,

V = Et + E₀(d-t)

=> V = E₀t/k + E₀(d-t)

=> V = E₀(d - t + t/k)

we know that, E₀ = q/ε₀A

=> V = q(d - t + t/k)/ε₀A

=> C = q/V

=> C = ε₀A/(d - t + t/k)

which is the required expression for capacitance,

2) A metallic plate of thickness t is inserted,

when a conducting metallic plate is inserted then electric field inside the plate will be zero

=> E = E₀/k = 0

=> k = ∞

hence putting the value of k in the above equation we get,

C = ε₀A/(d - t)

which is the required expression for capacitance with metallic plate

Answer 2

Answer:

ब्याज दर 5% है।

Step-by-step explanation:

हल:-

मूलधन (P) = ₹ 1000;

मिश्रधन (A) = ₹ 1102.50;

समय (n) = 2 वर्ष

दर (R) = ?

$\bf∵ \: मिश्रधन = मूलधन \times \bigg(1 + \frac{दर}{100} \bigg) ^{n}$

$\bf \therefore \: 1102.50 = 1000 \times \bigg(1 + \frac{R}{100} \bigg) ^{2}$

$\rm \longrightarrow \: \frac{11025}{10 \times 1000} = \bigg(1 + \frac{r}{100} \bigg) ^{2}$

$\rm \longrightarrow \: \frac{441}{400} = \bigg(1 + \frac{r}{100} \bigg )^{2}$

$\rm \longrightarrow \: \bigg( \frac{21}{20} \bigg) ^{2} = \bigg(1 + \frac{r}{100} \bigg) ^{2}$

$\rm \longrightarrow \: \frac{21}{20} = 1 + \frac{r}{100}$

$\rm \longrightarrow \: \frac{r}{100} = \frac{21}{20} - 1$

$\rm \longrightarrow \: \frac{r}{100} = 1 + \frac{21 - 20}{20}$

$\rm \longrightarrow \: \frac{r}{100} = \frac{1}{20}$

$\rm \longrightarrow \: r = \cancel{\frac{100}{20} }$

$\rm \longrightarrow \: r = 5\%$

अतः, ब्याज दर 5% है।