A 100 W resistor is connected to a 220 V, 50 Hz ac supply.
(a) What is the rms value of current in the circuit?
(b) What is the net power consumed over a full cycle?
Resistance of the resistor, R = 100 Ω
Supply voltage, V = 220 V
Frequency, ν = 50 Hz
(a) The rms value of current in the circuit is given as
\(I=\frac{V}{R} = \frac{220}{100} = 2.20A\)
(b) The net power consumed over a full cycle is given as:
P = VI = 220 × 2.2 = 484 W
The alternating current \( I \) in an inductor is observed to vary with time \( t \) as shown in the graph for a cycle.

Which one of the following graphs is the correct representation of wave form of voltage \( V \) with time \( t \)?}
Rishika and Shivika were partners in a firm sharing profits and losses in the ratio of 3 : 2. Their Balance Sheet as at 31st March, 2024 stood as follows:
Balance Sheet of Rishika and Shivika as at 31st March, 2024
| Liabilities | Amount (₹) | Assets | Amount (₹) |
|---|---|---|---|
| Capitals: | Equipment | 45,00,000 | |
| Rishika – ₹30,00,000 Shivika – ₹20,00,000 | 50,00,000 | Investments | 5,00,000 |
| Shivika’s Husband’s Loan | 5,00,000 | Debtors | 35,00,000 |
| Creditors | 40,00,000 | Stock | 8,00,000 |
| Cash at Bank | 2,00,000 | ||
| Total | 95,00,000 | Total | 95,00,000 |
The firm was dissolved on the above date and the following transactions took place:
(i) Equipements were given to creditors in full settlement of their account.
(ii) Investments were sold at a profit of 20% on its book value.
(iii) Full amount was collected from debtors.
(iv) Stock was taken over by Rishika at 50% discount.
(v) Actual expenses of realisation amounted to ₹ 2,00,000 which were paid by the firm. Prepare Realisation Account.
A carpenter needs to make a wooden cuboidal box, closed from all sides, which has a square base and fixed volume. Since he is short of the paint required to paint the box on completion, he wants the surface area to be minimum.
On the basis of the above information, answer the following questions :
Find \( \frac{dS}{dx} \).

When voltage changes its direction after every half cycle is known as alternating voltage. The current flows in the circuit at that time are known as alternating current. The alternating current(AC) follows the sine function which changes its polarity concerning time. Most of the electrical devices are operating on the ac voltage.
