The Ideal Operational Amplifiers - GATE EE Analog and Digital Electronics

 The minimum no of pins required by dual-op-amp is 8. Each op-amp has 2 input terminals(4 pins) and one output terminal(2 pins). Another 2 pins are required for power.
Similarly, The minimum no of pins required by dual-op-amp is 14: 4*2 + 4*1 + 2 = 14.

An ideal operational amplifier does not has a zero input impedance.

V_c = 0.5(V₁ + V₂) and
V_{d = V2 – V1.}

Output voltage (v_o​) = 4 V,

Input voltage (v_i​) = 2 V.

• v₊​ = v_i ​= 2V, as the non-inverting terminal is directly connected to the input voltage (v_i​).
• The voltage v_at the inverting terminal is determined by the resistive divider formed by 1MΩ and 1 kΩ.

Using the voltage divider rule:

Substitute v_o​ = 4V:

Step 3: Calculate the Gain

From the op-amp equation:

There are three terminals for the operational amplifier.

It is another way to refer to op amps based on its terminal characteristics.

Option D is correct.

From Option D: V_d = V₂ - V₁ and V_c = 0.5(V₁ + V₂).

Multiply the common-mode equation by 2: 2V_c = V₁ + V₂.

Use the differential equation: V_d = V₂ - V₁.

Add the two equations: 2V_c + V_d = 2V₂, so V₂ = V_c + V_d/2.

Subtract the differential equation from the doubled common-mode: 2V_c - V_d = 2V₁, so V₁ = V_c - V_d/2.

Therefore, V₁ = V_c - V_d/2 and V₂ = V_c + V_d/2, consistent with Option D.

The minimum no of pins required by dual-op-amp is 8. Each op-amp has 2 input terminals(4 pins) and one output terminal(2 pins). Another 2 pins are required for power.

Only option d does not satisfies the mathematical relation between the given quantities.

 These units are obtained from the definition of the term slew rate.